
Class 


t) Fh- ^ ^ 


Book 


-ds 


ma 

PRKSENTi;]) !5Y ' / 







Digitized by the Internet Archive 
in 2011 with funding from 
The Library of Congress 



http://www.archive.org/details/correlationsofme01simp 



CORRELATIONS OF MENTAL 
ABILITIES 



BY 
BENJAMIN R. SIMPSON, 



Submitted in partial fulfilment of the requirements 
for the degree of Doctor of Philosophy, in the 
Faculty of Philosophy, Columbia University. 



PUBLISHED BY 

Wtatlitrs (SnlUgp, (Eolumhla llninpraitB 

NEW YORK CITY 
1912 






Copyright, 1912, by Benjamin R. Simpson 






i 






CONTENTS 

Sec. page 

I. The Problem and Its Importance i 

II. General Method of the Investigation 3 

1. Abilities tested 3 

2. Tests used 5 

3. Subjects 5 

4. Method of giving the tests 7 

III. The Administration of the Tests in Detail 8 

X. Order of giving the tests 8 

2. Instructions given in each variety of test 8 

3. Individual dififerences in ability to interpret instructions 11 

IV. Scoring of Results 12 

1. General principles 12 

2. Method of scoring for each test, and rehability of the 

score given 13 

y. Reliability of the Measures Secured by Use of the Tests 35 

1. The two different methods used in treating the correla- 

tion data 35 

2. Detailed discussion of the reliability of each test 43 

VI. Significance of the Tests and Analysis of ' General 
Intelligence'' as Shown by Differences Between 

the ' Good ' a.nd the ' Poor ' Groups 53 

1. Extent of overlapping in the different tests 53 

2. The mental relationships revealed by the Pearson co- 

efficients of correlation 55 

3. Grouping of the tests according to the mental relation- 

ships shown by the correlation coefficients 65 

(i) Tests of selective thinking 65 

(2) Memory tests 65 

(3) Association tests 65 

(4) Perception tests 65 

(5) Motor control 66 

(6) Discrimination of lengths 66 

4. Order in which abilities correlate with other abilities 

tested 66 

5. Analysis of the individual differences revealed by the 

tests, and evidences that they are largely due to 

differences in native mental capacity 67 



iv Contents 

PAGE 

VII. Comparison of Results With Those of Other Investi- 
gators 75 

Wissler, Aikens and Thorndike, Norsworthy, Terman, 
Binet, Spearman and Krueger, Spearman, Thorndike, 
Burt, Bonser, Brown 

VIII. Conclusions 109 

Bibliography iii 

Appendix. Descriptions of tests used 112 



LIST OF TABLES 

PAGE 

la, lb, In. Original Scores Awarded 19-29 

II. Total Scores Awarded and Scores in First and Second 

Trials 30-33 

III. Rank of Subjects in the Different Tests 34 

IV. Illustration of the Methods of Treating Correlation Data. . 36 
Va. Deviations from the Median of the Good and Poor Sub- 
jects Combined 39 

Vb. Deviations from the Median of the Good Subjects only. . . 40 

Vc. Deviations from the Median of the Poor Subjects only. . . 40 
VI. Deviations from the Median, First and Second Trials, All 

Subjects Combined 41 

VII. Reliability of the Tests 42 

VIII. Extent to which the Poor Group Overlaps the Good Group 52 

IX. Pearson Coefficients of Correlation, Raw 56 

X. Pearson Coefficient of Correlation, Corrected for Attenu- 
ation 58 

XI, XII and XIII. Pearson Coefficients of Correlation Used in 

Correcting Raw Coefficients . . . . •. S9-61 

XIV. Deviation Measures Inferred from Per Cents of Judg- 
ments of Superior 63 

XV. Ranks of Good Group for Estimated Intelligence 72 

XVI. Deviation Measures Inferred from Per Cents of Judg- 
ments of Superior 74 

XVII. Some Results of Binet's Experiments 80 

XVIII. Ranking of Pupils in Binet's Experiments 80 

XIX. Oehrn's Results 81 

XX. Bonser's Results 102 



CORRELATIONS OF MENTAL ABILITIES* 

I. The Problem and Its Importance 

What constitutes general intelligence? How can we measure 
its amount? These are questions of immense practical impor- 
tance as well as of theoretical interest. Men in every line of 
activity are called upon every day to pass judgment upon the 
mental capacity of individuals and of groups. In many cases 
a choice must be made between a number of applicants of vary- 
ing degrees of capacity and fitness. Other things being fairly 
equal, the matter of prime importance for the judge to discern 
is the general mental ability of each of the persons in ques- 
tion. This judgment must be made in one of three ways: (i) 
by the examinations the candidate has passed and the certificates 
he has gained as a result of definite study; (2) by the opinions 
or recommendations concerning the candidate, given by those 
who know him and his work; (3) by the general impression 
gained from the way the candidate conducts himself during the 
course of the interview. We shall not dwell upon the inade- 
quacy of these tests as a means of determining the general in- 
telligence of an individual. The first, at best, gives a measure 
of the candidate's attainments along the lines tested, and only 
indirectly and secondarily gives an indication of his ability. The 
second and third are subject to all the inaccuracies of unscien- 
tific and ill-grounded personal opinion. Much as we need to 
get the right people into the right places, comparatively little 
has been done to replace these empirical methods by scientific 
ones. 



*The problem of this research was suggested and outlined by Professor 
E. L. Thorndike, and indebtedness is cheerfully acknowledged to him for 
a teacher's guidance and help in every difficulty. The work as carried out 
has been somewhat less comprehensive than that originally suggested. 

Grateful acknowledgment is also due the seventeen professors and stu- 
dents of Teachers College who acted as members of the " Good " group 
of subjects, to Miss Rusk for assistance in scoring a number of the 
records, and to Dr. Whitley. 

For the conclusions stated, the writer alone is responsible. 

I 



2 Correlations of Mental Abilities 

The same holds true with regard to school determinations of 
ability. Certificates, degrees, and the like, of all grades of im- 
portance are given on the basis of demonstrably inadequate 
measures of mental capacity or amount of training, and later 
offered as valid measures of either or both. Students of educa- 
tion have felt the inadequacy of the old time methods to 
diagnose and measure with any degree of accuracy the real abili- 
ties of the pupil, and students of psychology have, beginning 
with Galton, been devising tests of mental capacities both special 
and general. This work has been summarized in Whipple's 
"Manual of Mental and Physical Tests" ('lo), from which 
may be gained a just notion of the range of experimentation, the 
mistakes and improvements, and the present hopeful status of 
intellectual diagnosis by objective tests. The early workers 
along the line of devising mental tests for the measurement and 
diagnosis of general intelligence now see their labors justified 
by practical results. The period of discouragement and tem- 
porary defeat in the use of this method has been passed, and 
the time has come when workers in this field can go ahead with 
confidence that in due time results of much practical importance 
will be secured through painstaking and intelligent investigation. 
Once a series of mental tests can be perfected that will en- 
able us to determine the nature and amount of a person's mental 
capacity with a fair degree of accuracy, a corner stone will have 
been laid toward the foundation of a science of education. As 
yet we are not in a position to do justice either to the exception- 
ally bright or the exceptionally dull pupils, to say nothing of 
pupils of smaller degrees of variation from the average. We 
have as yet perfected no scientific method of picking out excep- 
tional children, and until we have adequate means of doing this, 
we cannot expect to have their respective needs properly pro- 
vided for. 

But can we hope to find the means of classifying pupils in 
this way, according to the degree of their intelligence ? The an- 
swer to this question is to be found in the results that have al- 
ready been achieved by the use of even such imperfect tests as 
the Binet-Simon Tests of Intelligence. Already they are being 
successfully used and widely adopted in schools for the feeble- 
minded, to determine the mentality of the subject and the conse- 



General Method of the Investigation 3 

quent treatment. They have been adopted in New Jersey as 
a means of diagnosis for retarded children. They have been 
used in courtroom procedure in New York City for the pur- 
pose of ascertaining the mental status of a youthful criminal, 
with a view to determining to what extent he should be held 
accountable for his conduct, and the sort of education he should 
subsequently receive. And this is only a crude beginning. In 
America alone the work of perfecting and extending such tests 
is being energetically pushed forward by Goddard in New 
Jersey, Wallin in the University of Pittsburgh, Huey in Johns 
Hopkins University, Terman in California, and others. Similar 
tests are being used elsewhere, such as the Sante De Sanctis 
tests in Italy. The more attention is given to studying the tests 
themselves, and developing new tests of greater convenience, re- 
liability and significance, the greater will be the practical educa- 
tional results. 

This monograph is a contribution to knowledge of individual 
differences, especially in that complex of qualities which we call 
' general intelligence,' and of the means of measuring them. Its 
special purpose is to determine the significance of certain tests 
by showing what relations they have to one another and to gen- 
eral intelligence in its common meaning. On the other hand, 
variations in general intelligence, as imputed to this, that and 
the other individual by the world's judgment, will themselves be 
better understood by the discovery of their relations to achieve- 
ment in these tests, 

II. General Method of the Investigation 

I. Abilities tested 

The general method of the investigation was to select tests 
of a variety of mental abilities, which may be grouped roughly 
under six headings, namely, sense-discrimination, motor-control, 
efficiency in perception, efficiency in association, memory, and 
what, for lack of a better term, I shall call abstraction or selec- 
tive thinking. Of course, all of these abilities may involve com- 
mon elements to a greater or less extent. On the other hand, 
each test is a test of a specific thing. For instance, the tests of 
perception are tests of a specific and limited kind of perception, 
under particular and limited conditions — to mark the A's or 



4 Correlations of Mental Abilities 

the B's on a blank like that on page 112, and to mark the hexa- 
gons and halfcircles on a blank like that on page 113. If the 
test turns out to be a reliable one, that is, if two trials of the 
same test correlate highly with each other in a group of persons, 
it is evident that something definite in the way of ability has 
been tested. Whether or not the ability tested is accurately 
named, is a matter of secondary consideration at the outset. For 
instance, if we give two trials of the "A test " (marking as rap- 
idly as possible all the A's on a printed page), to each member 
of a group of a hundred persons, and find that the order of ex- 
cellence in the first trial is closely the same as it is in the second 
trial, — or in other words, that the two trials correlate very 
highly with each other— it is evident that the records secured 
are measures of some definite ability, even though we may not 
be sure that that ability is accurately named efficiency of per- 
ception.^ 

Again if two trials with the Easy Opposites test should prove 
similarly to test some one and the same thing, and if there 
should turn out to be a positive correlation of 50 per cent or more 
bttween the A test and the Easy Opposites test, it is evident that 
we have measured a mental relationship between dififerent abili- 
ties, even though we may not yet be able to say with scientific 
accuracy that one is a test of perception and the other a test 
of association. However, the accurate naming of general abili- 
ties should be aided by the gaining of measures of relationship 
between different mental tests. For instance, if the A test and 
the Geometrical Forms test (marking all the geometrical forms 
of a certain kind on a page of printed geometrical forms), cor- 
relate almost as highly with each other as two records of the 
A test correlate with one another, it is evident that the two 
tests — A test and Geometrical Forms test — measure very much 

^ The experimental work was done in 1907, but for various reasons pub- 
lication has been delayed. Since the writer undertook the investigation 
important studies of a similar sort have been made — notably those of 
Thorndike ('09), Burt ('09), Bonser ('10), Whipple ('10), Whitley ('11), 
and Woodworth and Wells ('12). If these studies had been available then, 
the writer could have altered and much improved the tests which he used. 
But at that time the work on the significance of tests was practically only 
that summarized by Thorndike ('03), and Spearman ('04), all done before 
the discovery of ' attenuation ' by the variability of the result of a few 
trials from that true for an individual on the whole ; and two studies by 
Spearman ('04) and by Krueger and Spearman ('06). 



General Method of the Investigation 5 

the same ability, and that they are properly classed under the 
same general heading, in this case perception. 

2. Tests 

The tests used, fifteen in all, are described in detail in the ap- 
pendix on pages 112 to 122. They included two of perception — 
marking A's and marking geometrical forms ; three of memory 
— memory of unrelated words (auditory), memory of passages 
(auditory), and recognition of twenty-five forms studied, 
amongst fifty shown later; four of association — addition, easy 
opposites, associating words with hieroglyphic forms in pairs, 
and adding letters to make ba, ca, . . . be, ce, etc., into 
words (referred to as the ha or Completing Words test) ; three 
of selective thinking — the hard opposites, the Ebbinghaus or muti- 
lated text, and the absurdities test; two of sense discrimination 
— drawing lines each equal to a given length, and estimating the 
comparative lengths of pairs of lines; and one of motor control 
— the scroll test. Most of these tests had been used at Columbia 
University. 

3. Subjects 

As to the persons selected as subjects to be tested, the general 
plan was to take two groups of adults, representing as far as 
possible the two extremes of * general intelligence ' as judged 
by the world. The group representing the high grade of intel- 
lectual efficiency — hereafter called the Good group — was made 
up of seventeen professors and advanced students of Columbia 
University. That the persons making up this Good group repre- 
sent a high degree of mental ability and efficiency is evidenced 
by the number who have since attained high positions in the 
teaching profession. At least five of the thirteen who were then 
graduate students have since secured university positions, and 
others are holding positions almost, if not equally, responsible. 

It is safe to say that if an omniscient judge should rank the 
half million teachers of the country in order for ' general intelli- 
gence,' at least three of the seventeen would be put in the high- 
est hundredth of them, and at least ten, very likely all, of the 
seventeen, in the highest tenth of them. It is also the case that 
the seventeen would rank far above the average man in the 
management of affairs. 



6 Correlations of Mental Abilities 

Those in the group representing the low grade of efficiency 
were twenty in all, selected from men in New York City who 
had never held any position demanding a high grade of intelli- 
gence. All were of mature age and fairly comparable in that 
respect with the members of the Good group. In order that 
none should be at a decided disadvantage in the language tests, 
none were selected who did not speak English as their mother 
tongue. Two of them were persons earning comfortable livings 
for their families, but men recognized by their associates as 
being dull. Eleven others were staying at the Salvation Army 
Industrial Home at the nominal salary of $i per week in addi- 
tion to board and room, until work could be secured. One of 
these held a somewhat responsible position at the time, acting 
as assistant superintendent of the Home. He stood high in the 
most significant tests. The subject who did poorest of all was a 
man twenty-four years of age who had been at the Home for 
four years, and was quite content to remain there indefinitely 
on the permanent wage of $i a week besides board and lodging. 
The remaining seven were found in a mission on the Bowery 
where they were being helped somewhat until they could find 
employment. Altogether there were thirty-seven subjects, seven- 
teen in the Good group, and twenty in the Poor group. 

From the way in which those in the Poor group were selected, 
it is clear that they represent persons of a low grade of intel- 
lectual efficiency. They are, with the two exceptions noted 
above, persons who for some reason were out of employment. 
In some cases, no doubt, the lack of employment may have been 
partly due to habits of intemperance, but this defect would in 
most instances be insufficient to cause discharge if the man were 
otherwise above the average in efficiency. Nor would such cases 
be common in these religious establishments. In my opinion 
these twenty men were as temperate in respect to alcohol as the 
average New York male. 

Most of the Poor subjects had worked at several different 
occupations. The facts, as far as obtained, were as follows : 
Brakeman, clerk, timekeeper ; soldier, cook ; teamster ; wood 
worker, help on boats, hostler; machinist; worker in silk fac- 
tory, insurance broker, janitor; clerk, office help; shoe-laster; 
painter; clerk, teamster; help in customs house, night watch- 



General Method of the Investigation 7 

man, checker on ship ; hand in shoe factory ; blacksmith, crock- 
ery business ; salesman, collector of accounts ; cook, mechanic ; 
seaman, general help, cook, farm laborer; foreman of milk busi- 
ness; wagon painter; farmer's help, employee in knitting fac- 
tory; printer's help, driver of express wagon. 

The three who seemed the slowest and dullest of all, were 
the two who had regular employment but had been mentioned 
to the writer as being considered dull by their associates — the 
foreman of the milk business and the wagon painter — and the 
young man of twenty- four who was quite content to stay indefi- 
nitely at the Salvation Army Industrial Home. 

4. Method of giving the tests 

The tests were all given individually in the same order and 
as nearly as possible in the same way. To avoid fatigue, they 
were given at two sittings, except in about three cases with per- 
sons of the Good group, where they were completed in compara- 
tively short time and with no visible signs of fatigue. The time 
taken to complete the tests varied from about three to five or 
six hours. Those doing them most quickly secured on the whole 
by far the best records for accuracy as well. 

The zeal with which the subjects undertook the tests is beyond 
question a matter to be carefully considered. This seemed to 
the writer as satisfactory as could reasonably be expected. In 
the case of the Good group all were eager to do their best be- 
cause of interest in the tests and their results for science. In 
the case of the Poor group, with the exception of two or three, 
the same was true, although perhaps to a somewhat smaller 
extent. At first a little difficulty was experienced in getting per- 
sons of this class to take the tests. Those at The Salvation 
Army Industrial Home were in some cases at first a little diffi- 
dent about it. They seemed to fear that their mentality might 
be subjected to a rather minute diagnosis. However, as soon 
as it became known at the Home that all of those selected were 
to be paid a certain amount " to complete the course," and that 
there was nothing very extraordinary about the tests, they were 
willing to do their best to give satisfaction, and also were eager 
to make good records. Only two of the whole thirty-seven 
(Good and Poor) seemed to find the tests irksome before the 



8 Correlations of Mental Abilities 

finish, viz., number thirty-five who complained that his eyesight 
handicapped him, and number thirty-seven who showed little 
evidence of interest in any of the tests. This was probably due 
to the fact that he had little interest in anything at all intel- 
lectual. There is no doubt that number thirty-five was handi- 
capped in most of the tests, and especially in those of perception, 
by poor eyesight; and possibly physical fatigue influenced his 
results, as he had worked all day at his trade of wagon-painting. 
A number of those on the Bowery seemed to do their best because 
of an idea that the discovery of unexpected talent might lead to 
the offer of a good position. 

III. The Administration of the Tests in Detail 

1. Order 

A copy of each test used is given in the appendix on pages 
112 to 122. The name used hereafter in speaking of the test 
is also given there, as well as brief general directions to the sub- 
ject about to take the test. The reader is therefore advised 
to turn to the appendix at this point for this information. The 
order in which the tests were given is the order in which they 
follow each other in the appendix. Some of the easier tests, 
such as those of perception, were given first so that the Poor 
subjects might not become discouraged at the outset. 

2. Instructions 

As far as possible, the instructions for any particular test 
were the same for all subjects. But on account of the wide 
differences between some members of the Poor group and the 
members of the Good group, it was necessary to give more de- 
tailed instructions to the Poor subjects, to insure that they 
understood beforehand exactly what they were required to do. 

In giving the A test, the subject was allowed to glance at 
the page of printed capitals, and was then told to take up the 
paper as soon as the signal was given, and mark all the A's 
as quickly as possible with a pencil, in any manner most con- 
venient to himself. The time was taken with a stop watch. The 
second trial consisted in giving him a new copy of the test with 
instructions to mark all the B's as rapidly as possible. In the 
second test — Geometrical Forms — the instructions were similar, 



The Administration of the Tests in Detail 9 

except that special pains were taken to make sure that the sub- 
ject understood clearly what sort of geometrical form was to 
be marked. To insure this, he was allowed to glance for a mo- 
ment at the printed slip, and then told to mark only the hexagon 
with the point up. This was further illustrated by drawing the 
hexagon to be marked on a separate piece of paper. In the 
second trial it was similarly made clear that the figure to be 
marked was the half-circle with the Hat side up, and not the 
half-circle in any other position. In taking the Scroll test of 
motor-control, the same fountain pen was used by all of the 
subjects. The directions given for the first trial were: " Trace 
the white part of the spiral as rapidly as possible without touch- 
ing the black part." As the time taken for the first trial varied 
to a considerable extent, on the second trial the subject was re- 
quested to go either faster or slower than before so as to make 
the time occupied in the second trial about three minutes. 

In the Easy Opposites test, the subject was required to give the 
opposite of the printed word orally, instead of by writing it, 
so that the test would be a measure of quickness of association 
rather than a measure of quickness of writing. The instructions 
were : "As quickly as possible give orally a word that means 
the exact opposite of the word in the list. Thus if you see the 
word small, say large, and so on down the list." 

In the Recognizing Forms test, the subject was allowed to 
glance for a moment at the two sheets. It was then explained 
that he would be given one minute in which to study the small 
sheet, and that at the end of that time, he would be asked to 
mark on the large sheet only those forms that were exactly the 
same as the ones he had seen on the small sheet. In both cases 
subjects were given all the time they desired to mark the forms 
on the large sheet. 

In giving the Memory of Words test, it was explained that 
a list of simple words would be read aloud once, and that as 
soon as the last word was heard, the subject was to write down 
in any order as many of the words as he could remember. 

In the Pairs test — connecting a word with a hieroglyphic form 
— the subject was allowed to glance at a sheet containing the 
forms only, and another sheet with the forms and words in 
pairs. He was then told that he would be given one minute in 



lo Correlations of Mental Abilities 

which to study the second sheet, so that when the forms only 
were given he could write down for each, the corresponding 
word. In the last two of the four trials given, one and a half 
minutes were allowed in which to study. 

In the Memory of Passages test, care was taken always to 
read at a uniform rate and as distinctly as possible. Two or 
three of the Poor group complained that they could not spell 
well enough to write down the substance of the passage heard. 
In such cases the experimenter took down the substance as the 
subject gave it oralty. 

In giving test IX — Drawing Lengths — the subject was allowed 
to draw each line on the page of a ruled exercise book, but 
each of the lines he drew was covered up before drawing the 
next line, to insure that each drawing was an estimate of the 
original length and not a copy of the first line drawn. 

In giving test X — Estimating Lengths — two horizontal lines 
of nearly equal length were drawn side by side on a piece of 
cardboard. They were heavy lines drawn with a drawing pen 
and India ink, so that they could be clearly seen and easily com- 
pared. There were four sets of cards, with eight exactly alike 
in each set. In the first set the difference in length in the two 
lines was 8 mm., one lOO mm. and the other io8 mm. In the 
second set the lines were lOO and io6 mm. respectively; in the 
third set lOO and 104 mm., and in the fourth set 100 and 102 
mm. In giving the test each cardboard was shown in turn to 
the subject, and he was asked simply, " Which is the longer of 
the two lines ? " The whole test was then repeated, so that in 
all there were 16 estimates of each of the four lengths of this 
test. The subject was allowed all the time he wished to decide 
in every case, but little seemed to be gained by much hesitation 
in deciding. 

In test XI, Addition, the subject was allowed to glance at 
the addition examples, and was instructed to turn over the paper 
and start adding as soon as the signal was given, to add as 
quickly and accurately as possible, putting down the results as 
he proceeded. 

In test XII, Hard Opposites, the instructions were the same 
as in the Easy Opposites test, except that the subject was told 



The Administration of the Tests in Detail ii 

to write down the opposite of the printed word, instead of giving 
it orally. Unless the word was utterly unknown to him, he was 
to take pains to write down the most accurate opposite he could. 

In test XIII, Completing Words, or '" ba test," besides the 
general directions indicated in the appendix, the subject was 
shown by an example what was to be done. 

To insure clear understanding of what was to be done in 
the Mutilated Text or Ebbinghaus test, a special sample was 
shown, and the blank spaces were filled in for him with ap- 
propriate words. 

In giving the last test. Absurdities, the instructions were, 
" Mark each sentence that contains an absurdity or impossibility. 
For instance, if a sentence stated or implied that lead was float- 
ing on water, mark such a sentence as absurd or impossible. Do 
not mark the sentences that contain no absurdity or impossi- 
bility." 

3. Individual differences in ability to interpret instructions 

Before giving the tests to any of the thirty-seven subjects 
whose records were secured, the experimenter took the precau- 
tion to practice himself in giving the tests to other persons, both 
for the purpose of acquiring the necessary skill in giving the 
tests in a uniform manner, and in order to determine the specific 
instructions necessary to be given to the subjects. Every 
reasonable precaution was taken to see that the instructions were 
understood before the test was begun, but in spite of this fact 
several of the poor subjects failed to follow instructions ex- 
actly. In some instances this seemed due to the fact that, though 
the instructions were understood when given, a part of them 
were forgotten as the work proceeded. In marking geometrical 
forms — test II — several of the Poor group started in by mark- 
ing only the hexagons with the point up, but before they got 
half way down^the page were marking all hexagons — with flat 
side up as well as with the point up. As the test was intended 
to be one of quickness in picking out forms and not one in 
ability to understand and remember instructions, they were not 
severely penalized for this.^ In three or four other cases it 
seemed fairly evident that the instructions were not perfectly 
^ See later account of methods of scoring. 



12 Correlations of Mental Abilities 

grasped before beginning the first trial, even though both sub- 
ject and experimenter thought that they were. For instance 
three of the dullest of the Poor group in doing test XIV, Ebbing- 
haus mutilated text, put several words in a single blank space 
where the sense seemed to them to require it, although they 
were distinctly told beforehand to put only one. Thus incident- 
ally the tests gave the experimenter an opportunity to form an 
estimate of each subject's ability to comprehend instructions. 
No attempt has been made to correlate this accurately with 
abilities as indicated by the tests themselves, but from memory 
of individual cases the writer is very confident that in general 
those who were dullest in comprehending and remembering in- 
structions were also poorest in the tests which later results 
proved to be most closely correlated with intelligence. In two 
cases a zero record — in test VII, Learning Pairs, — ^in the first 
of the four trials resulted from the fact that the subject took it 
for granted that the figures would be arranged in the same 
order on both the study slip and the test slip. He thus at- 
tempted to learn only the words in their correct order, instead 
of connecting the form with the corresponding word. How- 
ever, irregularities of this kind were of such slight consequence 
as not to interfere to any appreciable extent with the general 
results. 

IV. Scoring of Results 
I. General principles 

Any method of scoring the results of tests such as these must 
be more or less arbitrary. The method of scoring finally adopted 
was that which seemed fairest on the ground of common sense, 
and that which seemed to vary as little as possible from the re- 
sults secured by other reasonable methods of scoring. The 
original results which would take some scores of pages to 
print are all on file at Teachers College, so that any one who 
cares to do so can compare the final scores adopted here with 
those obtained by any other method of scoring that seems to 
him advisable, or test any of the writer's conclusions by com- 
puting the results by the different scoring. 



Scoring of Results 13 

2. Method of scoring for each test, and reliability of the score 

given 

The final score in the A test was got by taking the time in 
seconds required to complete the test, plus five seconds for each 
letter omitted. Thus the lowest score represents the greatest 
efficiency. As the average time for marking each of the fifty 
A's was not much under three seconds, it seemed fair to penalize 
each omission by something more than three seconds. On the 
other hand, if much more than five seconds were added for each 
omission, it would emphasize care and accuracy rather than 
quickness of perception. Moreover, it made little difference 
whether three, four, or five seconds were added for each omis- 
sion, judging by the average displacement of rank of the dif- 
ferent subjects. The average displacement in rank for each sub- 
ject owing to the difference in scores when four seconds are 
added for each omission, and when five are added, is only a 
trifle over one. The average displacement in case of adding 
three seconds for each omission and in adding five seconds for 
each omission is only two. Although this test is satisfactory in 
reliability, the average displacement in rank between the first 
trial (marking A's) and the second trial (marking B's) is 
slightly more than five. Thus the method of scoring adopted 
seems quite satisfactory. There were no errors of any kind in 
this test except omissions. 

For similar reasons the method of scoring the Geometrical 
Forms test was to take the number of seconds and add three 
for each omission in the first test, and six for each omission in 
the second. There were more than twice as many hexagons 
to be marked as half-circles. Hence it took about twice as long 
on the average to find and mark each half-circle as to find and 
mark each hexagon. Nothing was taken off for forms wrongly 
marked, since they were already penalized somewhat in that it 
took some time to mark the wrong form, and since if much were 
deducted for this, it would amount to making the test one of 
ability to understand instructions rather than one in quickness in 
picking out forms. 

The score in the Scroll test was got by taking the time in 
seconds and adding ten seconds for each touch of the black 



14 Correlations of Mental Abilities 

lines. Ten was selected as the number to be added for each 
touch, mainly because it equalized the scores of each subject 
in the two trials better than any other number. For instance, 
if five seconds instead of ten were added for each touch, the 
score in the second trial would be better than the score in the 
first trial in twelve cases, and poorer in twenty-five. If ten 
seconds were added for each touch, the score in the second 
trial would be better in eighteen cases, and poorer in nineteen 
than the first. If nine seconds were added, the second trial 
would be poorer in seventeen cases and better in twenty than the 
first. 

How much, if anything, should be allowed for improvement, 
it is very difficult to say, as it was not possible to keep either 
the time or the number of touches uniform in the two trials. 
Neither is it very helpful to estimate the average number of 
seconds that is equivalent to avoidance of one touch, as the 
variation is so very wide. In fact it seems difficult to find any 
system of scoring this test as given, that is altogether justifiable. 
On the whole it seems best to assume that the two trials are 
tests of the same thing, and that therefore that method of scor- 
ing is fairest which on the whole makes a given subject's first 
score and his second score as nearly equal as possible. Adding 
ten seconds to the time for each touch does this. 

For scoring the Easy Opposites test, the experimenter had 
kept track of the number of words that were correctly given, 
the number incorrectly given or omitted, and the number that 
could be considered half right. The score taken was the time 
in seconds, plus two seconds for a word half wrong, and four 
seconds for a word wrong or omitted. Notes were made at the 
time the test was given, of how much time a subject took to 
think up a satisfactory opposite for the one or two words that 
caused most hesitation or difficulty. This formed the basis for 
estimating how much on the average it was most just to add 
to the subject's time in seconds as a penalty for errors or omis- 
sions. 

In scoring test V, Recognizing Forms, one mark was allowed 
for each form correctly marked, and one was taken off for 
each form incorrectly marked. On this basis, if the subject 



Scoring of Results 1 5 

were merely guessing, his score would on the average approxi- 
mate zero. 

In test VI, Memory of Words, the score given was simply 
the number of words correct. Nothing was taken off in case a 
wrong word was written down. This, later study has shown to 
be unwise, but there were only a few such wrong words inserted 
and, as the labor of recalculating correlations and group dif- 
ferences would be very great, the scores have been left as origin- 
ally made. 

In test VII, Learning Pairs, the score given was simply the 
number of words right, except that there were a few instances 
where credit was given for a word half right, where the word 
was connected with the proper form but was not itself exactly 
correct. 

In scoring test VIII, Memory of Passages, the experimenter 
evaluated all of the records on a scale of from one to twenty- 
five. A month later he rated them independently a second time. 
An assistant in psychology also rated them independently. It 
was found that the three evaluations differed very little from 
each other. The average displacement in the rank of each sub- 
ject, according to whether he was ranked on the scoring of the 
assistant or on that of the experimenter's first scoring, was only 
about 2. The average change in rank between the experi- 
menter's first and second scorings was 2.3. As compared with 
this the average displacement of each subject in rank, between 
his score in the first two tests and his score in the last two, was 3. 

The score adopted in test IX, Drawing Lines, was the sum of 
the deviations plus and minus from the standard length. The 
constant error was separated out for study, but seemed to be 
of little significance, and so the deviation from the standard set 
was used. Out of the seventeen Good subjects only eight had 
a clearly positive error, and only four a clearly negative one. 

In test X, Estimating Lengths, each individual's number of 
correct judgments of each difference was recorded, and the indi- 
viduals ranked in order of merit accordingly. 

In scoring test XI, Adding, the time in seconds was taken 
and ten seconds added for each error. It was considered that 
the penalty should be estimated by the time that would probably 
be required to correct the error. This, in general, would be at 



1 6 Correlations of Mental Abilities 

least somewhat more than was required to do that part of the 
sum. On this basis at least five seconds should be added for 
each error and probably more, as the median time for doing a 
whole question, with a possibility of two errors, was about ten 
seconds. Whether six seconds or ten seconds is added for each 
error, makes very little difference; the average displacement in 
rank caused by this difference in scoring being only slightly over 
I. The difference in rank between a subject's score in his first 
trial and his second is on the average, 3.8. On the whole it 
seemed that ten seconds was a fair penalty for each error. 

In test XI, Hard Opposites, all of the words given as op- 
posites were collected and evaluated on a scale of from i to 4 
by three different persons, viz., two assistants in psychology and 
the experimenter. The three evaluations differed very little 
from each other, the average displacement in rank caused by 
using one rating rather than another being only slightly over i. 

The final score given to each subject was got by averaging the 
marks of the three different scorers, and then adding a certain 
number of seconds to the time score, as a penalty for each word 
wholly wrong or omitted, and a proportionate amount for a 
word partly wrong. On the basis of the time actually spent by 
a number of subjects to think up suitable opposites for the most 
difficult words rather than omit them, 36 seconds seemed to be 
about the right penalty for the total omission of a word. 

Other methods were tried, but none was found which on the 
whole seemed to equate the two factors of equality and speed so 
fairly, especially with reference to those who did best and 
poorest. For instance, an attempt was made to equate the time 
element and the quality element by combining the quality score 
with a reciprocal of the time score. This suggests itself on the 
general principle that if A does twice as much work as B in a 
given time, he deserves a score twice as high; if A and B do 
the same quality of work, and A takes twice as long as B, he 
is worth only half as much. The variations in the time, how- 
ever, were so great that such a method could not be fairly ap- 
plied without the use of complex mathematical calculations. 
Moreover it would assume that all of the words are equally diffi- 
cult, which of course is not the case. 

For somewhat similar reasons it was difficult to find a per- 



Scoring of Results 1 7 

fectly satisfactory method of scoring in test XIII, Completing 
Words, as in several cases there were a number of omissions 
whereas in other cases subjects had spent times varying greatly 
in amount in attempting to avoid omissions. On account of the 
large number of omissions, the second trial was thrown out al- 
together. For a similar reason the records of eight subjects 
were thrown out in trial one. The score given was the time in 
seconds plus 10 seconds for each error or omission. As far as 
could be judged, 10 seconds seem.ed to be the time that probably 
would have been required to complete the word. 

In reducing the results of test XIV, Ebbinghaus Mutilated 
Text, to a numerical score, they were first marked by the ex- 
perimenter as to excellence in filling out the blanks so as to 
make sense, regardless of the time taken. They were then 
marked in a similar way by an assistant in psychology, and 
then marked independently a second time by the experimenter. 
These three ratings, which did not differ materially from one 
another, were averaged so as to get the final rating for quality, 
i.e., ability to do the test without regard to the time taken. The 
average displacement in rank of each subject according to the 
different scorings was between i and 2. As it seemed just to 
count the time taken to do the test about equally with the 
quality of the work, the final score adopted was a combination 
of the time score and the quality score, weighting quality a little 
higher than time. In doing this the time factor taken was the 
reciprocal of one-fifth of the time in seconds. This method is 
not open to the same objections here as in the Hard Opposite 
test, and succeeds fairly well in equating speed and quality. 
However, the method may seem unnecessarily complicated, and 
could not very well be used except under special and limited 
conditions. It would have been less trouble, and about equally 
fair, to have held to the general method used in tests previously 
mentioned, namely, to take as the final score the time in seconds 
plus a certain penalty in seconds for each mark lost in the score 
for quality. 

In giving the Absurdities test it was assumed that the record 
could be scored simply by allowing i mark for each absurdity 
correctly marked, and taking off a mark for each one wrongly 
marked. This would give a score for quality, with which the 



1 8 Correlations of Mental Abilities 

time element could be combined to give a final score. It turned 
out, however, that the test as given was open to decided objec- 
tions, on account of containing a number of imperfections. Im- 
provements in the test will be discussed in another connection. 
As far as giving definite scorings was concerned, the test was 
finally thrown out. If, in spite of these imperfections, the re- 
sults are scored as originally intended, even regardless of the 
time element, it divides the two groups fairly well. 

The scores finally awarded to each individual in each test are 
given in Tables la to In inclusive. Each subject's total score in 
each test, and the scores in ist and 2nd trials of the test, are 
given in Table II. Table III gives the rank of each individual 
in each test. 



Scoring of Results 



19 



TABLE la 
Original Scores in Memory op Passages 



-8 
6 


+ 
m 


+ 
1-1 

m 


+ 


(N 
+ 

> - 


+ 

in 


+ 
m 


4- 

S2- 


+ 


1 


43 


44 


29 


36* 


43 


44 


31 


37* 


2 


44 


44 


31 


37 


45 


43 


37 


40 


3 


42 


41 


20 


30 


43 


42 


35 


38 


4 


42 


45 


28 


35 


44 


44 


37 


40 


5 


43 


44 


31 


37 


41 


43 


38 


40 


6 


38 


36 


24 


30 


43 


44 


39 


41 


7 


40 


42 


25 


33 


37 


40 


24 


31 


8 


33 


35 


19 


26 


35 


38 


27 


31 


9 


41 


29 


21 


28 


37 


34 


28 


31 


10 


43 


41 


21 


31 


40 


41 


30 


35 


11 


45 


43 


35 


39 


34 


38 


23 


29 


12 


42 


42 


29 


35 


37 


40 


32 


35 


13 


32 


27 


13 


21 


30 


27 


16 


22 


14 


29 


31 


13 


21 


32 


32 


18 


25 


15 


9 


14 


10 


10 


19 


17 


18 


18 


16 


36 


25 


16 


23 


37 


24 


23 


26 


17 


41 


41 


22 


31 


41 


43 


34 


38 


18 


21 


27 


12 


18 


26 


30 


25 


26 


19 


32 


20 


14 


20 


22 


17 


17 


18 


20 


32 


25 


18 


23 


31 


33 


26 


29 


21 


30 


25 


21 


24 


28 


33 


23 


26 


22 


8 


12 


6 


8 


9 


11 


9 


9 


23 


27 


23 


14 


19 


31 


24 


20 


23 


24 


21 


26 


11 


17 


27 


24 


20 


22 


25 


12 


16 


8 


11 


12 


15 


11 


12 


26 


17 


21 


10 


14 


22 


23 


18 


20 


27 


11 


13 


9 


10 


12 


11 


11 


11 


28 


16 


10 


9 


11 


15 


9 


9 


10 


29 


14 


14 


10 


12 


11 


9 


12 


11 


30 


21 


16 


15 


16 


17 


12 


11 


12 


31 


7 


8 


6 


6 


8 


7 


7 


7 


32 


15 


17 


10 


13 


8 


9 


8 


8 


33 


6 


8 


5 


6 


8 


7 


6 


6 


34 


20 


21 


15 


17 


6 


8 


5 


6 


35 


























36 


7 


6 


4 


5 


10 


9 


11 


9 


37 


3 


4 


3 


3 


1 


1 


2 


1 



Si (1±2) means sum of scores in passages 1 and 2 as scored by experimenter the first time. 
So ( 1 +2) means sum of scores in passages 1 and 2 as scored by experimenter the second time. 
Ri (1 +2) means sum of scores in passages 1 and 2 as scored by Miss R, an assistant in 
psychology. 

* Fractions have been omitted in these two columns. 



20 



Correlations of Mental Abilities 



TABLE lb 

Original Scores in Memory of Words 



TABLE Ic 

Original Scores 
IN A Test 



o 
O 




1 




s 




s 


4 


60 

c 
o 


73 

CO 

< 


a 
o 

o 
CO 


T3 


CO 

-^ 

O 

s 

.s 


6 


1 


6 


d 


. 6 


6 


6 
;z; 


1 


6 


6 


S 


6 


s 


1 


9 





9 





9 


2 


10 





50 


121 


50 


135 


2 


9 





11 





5 





9 





46 


80 


38 


77 


3 


9 


1 


9 





11 





9 


1 


49 


109 


39 


111 


4 


10 





9 





8 





9 





43 


86 


39 


84 


5 


5 





10 





5 


1 


8 


1 


47 


107 


44 


112 


6 


8 





10 


2 


9 


1 


11 


1 


50 


126 


49 


127 


7 


6 


1 


5 





5 





9 





41 


121 


47 


133 


8 


5 





6 


2 


6 





8 





50 


118 


47 


128 


9 


9 





8 





10 





9 





47 


129 


43 


135 


10 


6 


1 


7 





7 





7 





50 


100 


50 


120 


11 


9 





4 


1 


5 


1 


8 


1 


46 


78 


46 


95 


12 


8 


1 


8 





7 





6 


1 


48 


123 


48 


137 


13 


6 


1 


8 





6 


1 


7 





50 


92 


48 


92 


14 


5 





5 


1 


7 


1 


6 





47 


111 


40 


92 


15 


6 


1 


5 


1 


9 





9 





49 


127 


50 


123 


16 


9 





7 





7 





8 


1 


48 


129 


42 


118 


17 


8 





3 


1 


7 





5 





48 


138 


47 


136 


18 


6 


2 


6 


1 


5 





6 


1 


50 


lis 


49 


112 


19 


3 


4 


5 


1 


6 


2 


5 


1 


48 


115 


47 


114 


20 


8 


1 


5 


1 


6 





6 





46 


142 


46 


195 


21 


6 





5 





5 





5 


1 


19 


81 


41 


100 


22 


5 


1 


6 


1 


5 





5 





44 


107 


48 


90 


23 


8 





7 





6 





6 


1 


43 


162 


44 


171 


24 


6 





5 


1 


5 





4 





39 


81 


31 


84 


25 


5 





6 





4 


2 


4 


1 


29 


84 


44 


130 


26 


6 





2 


2 


4 


1 


6 


2 


50 


157 


49 


142 


27 


3 


2 


6 





3 


1 


3 


1 


45 


155 


43 


144 


28 


6 





6 


1 


3 


1 


5 





47 


162 


48 


165 


29 


5 


1 


4 





4 


1 


4 





30 


112 


38 


101 


30 


5 





4 


2 


5 





5 





35 


123 


44 


144 


31 


6 





4 





4 





2 


1 


46 


195 


43 


133 


32 


4 


1 


4 


2 


5 


2 


4 


1 


34 


92 


32 


83 


33 


4 


1 


3 





2 


4 


5 





18 


127 


40 


115 


34 


3 


2 


6 





4 


2 


1 


2 


50 


270 


48 


222 


35 








1 


1 


3 


1 


4 


2 


48 


268 


44 


280 


36 


6 


1 


3 


5 


4 


1 


5 





47 


130 


48 


134 


37 


5 





3 


2 


1 


4 


3 


2 


21 


127 


38 


128 



Scoring of Results 



21 



TABLE Id 



Original Scores in Adding 



TABLE le 

Original Scores in Geomet- 
rical Forms 



t5 

3 
CO 

6 


-1-3 
-a 

6 


H-l 

o 
6 


o 
o 

.S 

s 




o 

1 


CO 

Pi 
O 
o 
(P 
zn 

.S 

a 


5 
6 


1 

6 


13 

s 

O 
6 


CQ 

T3 
1=1 
O 
o 
cu 

Ul 

B 

a 


d 


a 
o 

u 

6 


a 
o 

6 


CO 

g 

o 

a 


1 


10 





54 


10 





43 


36 








81 


14 








83 


2 


7 


3 


55 


8 


2 


52 


33 





3 


44 


13 





1 


45 


3 


9 


1 


80 


8 


2 


85 


34 





2 


76 


13 





1 


76 


4 


9 


1 


82 


7 


3 


81 


24 





12 


75 


10 





4 


70 


5 


8 


3 


79 


9 


1 


81 


26 


2 


10 


82 


12 





2 


76 


6 


6 


4 


91 


9 


1 


84 


33 





3 


77 


12 





2 


66 


7 


8 


2 


91 


8 


3 


100 


33 





3 


89 


13 





1 


88 


8 


10 





58 


10 





63 


29 





7 


95 


14 








78 


9 


8 


2 


96 


10 





111 


31 





5 


80 


13 





1 


77 


10 


10 





92 


10 





94 


36 








75 


14 








70 


11 


8 


3 


71 


10 





64 


26 


2 


10 


58 


13 


1 


1 


69 


12 


8 


3 


65 


9 


1 


73 


27 





9 


91 


12 





2 


94 


13 


8 


2 


81 


9 


1 


89 


34 


4 


2 


56 


14 








70 


14 


10 





105 


9 


1 


124 


25 





11 


46 


12 





2 


44 


15 


9 


1 


82 


10 





84 


36 


13 





67 


13 





1 


79 


16 


7 


4 


106 


7 


4 


107 


32 


1 


4 


80 


13 





1 


80 


17 


9 


1 


116 


10 





136 


36 








90 


13 





1 


86 


18 


10 





74 


9 


1 


86 


30 


4 


6 


82 


14 


3 





103 


19 


10 





70 


10 





98 


35 


14 


1 


95 


14 








94 


20 


10 





153 


8 


2 


190. 


31 





5 


107 


10 





4 


127 


21 


6 


6 


202 


8 


2 


236 


32 





4 


79 


11 





3 


69 


22 


9 


1 


124 


8 


2 


154 


28 





8 


80 


13 





1 


76 


23 


4 


10 


81 


6 


6 


109 


34 





2 


170 


12 





2 


150 


24 


8 


2 


85 


6 


5 


85 


27 


2 


9 


93 


11 





3 


84 


25 


8 


2 


87 


9 


1 


93 


29 


7 


7 


107 


13 





1 


102 


26 


9 


1 


165 


8 


2 


151 


35 


12 


1 


107 


13 





1 


122 


27 


10 





131 


9 


1 


146 


33 


2 


3 


119 


12 





2 


93 


28 


9 


1 


157 


10 





140 


34 





2 


116 


9 





5 


113 


29 


7 


3 


75 


9 


1 


100 


30 





6 


90 


13 





1 


70 


30 


8 


2 


209 


10 





337 


31 





5 


104 


12 





2 


101 


31 


9 


1 


221 


7 


3 


224 


16 


8 


20 


102 


5 





9 


87 


32 


6 


4 


118 


6 


4 


132 


19 


1 


17 


67 


10 


9 


4 


78 


33 


10 





137 


10 





165 


22 





14 


89 


11 





3 


90 


34 


10 





273 


10 





273 


24 





12 


128 


12 





2 


105 


35 


9 


1 


149 


9 


1 


141 


31 


7 


5 


297 


13 


22 


1 


285 


36 


3 


7 


237 


7 


3 


295 


24 





12 


113 


13 


8 


1 


85 


37 


5 


5 


176 


4 


9 


217 


19 


2 


17 


106 


17 


16 


7 


127 



22 



Correlations of Mental Abilities 



TABLE If 



Original Scores in Learning Pairs 



TABLE Ig 

Original Scores in 
Recognizing Forms 



Id 
m 
o 




2 


T3 

a 

O 


4^ 


§ 


T3 
-t-i 

a 
o 


-a 


bC 

S 


a 

O 


+3 


o 


73 

a 

O 


'bb 


bX 

c 
S 


73 

'S 
o 




be 
C 

2 


-a 

'S 



6 


6 

!2; 


d 


6 
i2; 


6 


i 


6 


d 


d 


d 

;2; 


i 


d 


d 


d 


d 


d 


i_ 


6 

12; 


d 


1 


3 





7 


2 





8 


5 





5 


5 





5 


17 


1 


7 


15 


4 


10 


2 


7 


2 


1 


5 


3 


2 


8 





2 


4 


2 


4 


19 


2 


5 


9 


7 


16 


3 


9 


1 





10 








10 








9 


1 





15 





9 


13 


4 


12 


4 


1 


1 


8 


7 





3 


9 





1 


6 


2 


2 


13 


3 


11 


12 


1 


13 


5 


10 








7 


1 


2 


10 








10 








14 


2 


10 


11 


1 


14 


6 


i 





9 


7 


1 


2 


7 





3 


4 


2 


4 


13 


1 


11 


14 


3 


11 


7 


1 


2 


7 


4 





6 





2 


8 


2 


2 


6 


10 


1 


14 


12 


1 


13 


8 


4 


1 


5 


7 


1 


3 


9 





1 


9 





1 


11 


2 


13 


13 


1 


12 


9 


6 


1 


3 


7 


2 


1 


10 








7 





3 


16 


3 


8 


11 


2 


14 


10 


4 


2 


4 








10 


3 





7 


3 


1 


6 


13 


3 


11 


15 


7 


10 


11 


4 


4 


2 


1 


4 


5 


3 


2 


5 


3 


5 


2 


17 





7 


11 


3 


14 


12 


6 


1 


3 


7 





3 


8 


1 


1 


9 





1 


11 


3 


13 


9 


4 


16 


13 


5 


2 


3 


3 


2 


5 


8 





2 


8 


1 


1 


12 


3 


12 


17 


2 


8 


14 


4 





6 


2 


1 


7 


4 





6 


3 


1 


6 


10 


2 


14 


12 





13 


15 


7-1 





2 


5 


1 


4 


9 





1 


9 





1 


16 


1 


8 


14 


3 


11 


16 


6 


1 


4 


6 





4 


1\ 


2 


5 


1 


4 


18 


3 


6 


12 


3 


13 


17 


3 


1 


6 


3 


1 


6 


3 


2 


5 


4 


1 


5 


11 


4 


13 


14 


5 


11 


18 


2 


3 


5 


2 


6 


2 


2 


6 


2 


2 


7 


1 


9 


4 


15 


14 


8 


11 


19 


1 


2 


7 


2 





8 


2 





8 


2 


1 


7 


10 


1 


14 


11 


8 


14 


20 


1 


5 


4 


1 


2 


7 


1 


4 


5 





6 


4 


6 


2 


18 


13 


14 


12 


21 


1 


2 


7 


2 


2 


6 


1 


3 


6 


1 


1 


8 


7 


1 


17 


8 


5 


17 


22 


1 


4 


5 


2 


3 


5 


5 


1 


4 


2 


3 


5 


9 


4 


15 


12 


9 


13 


23 








10 


3^ 





6 


1 


2 


9 


1 





9 


2 


2 


22 


8 


1 


17 


24 


1 


1 


8 


1 


1 


8 


1 





9 


1 





9 


6 





18 


6 


2 


19 


25 


2 


2 


6 


2 


3 


5 


3 


1 


6 


3 


o 


5 


3 


8 


21 


9 


8 


16 


26 


1 


3 


6 


1^ 


2 


6 


1* 


4 


5 


2 


4 


4 


13 


11 


11 


12 


4 


13 


27 


3 


1 


6 




2 


7 


2" 


2 


6 


4 


1 


5 


7 


2 


17 


8 


4 


17 


28 





3 


7 




2 


7 





2 


8 


1 





9 


9 





15 


1 


1 


24 


29 


1 


1 


8 







8 


2 


1 


7 


1 





9 


6 


2 


18 


10 





15 


30 


2 


2 


6 




1 


8 





4 


6 


* 


2 


7 


12 


10 


12 


8 


8 


17 


31 


3 


3 


4 




4 


5 


3 


1 


6 


2 


3 


5 


11 


8 


13 


17 


8 


8 


32 





7 


3 





9 


1 


1 


6 


3 


1 


3 


6 


9 


5 


15 


11 


11 


14 


33 





1 


9 


1 


2 


7 





2 


8 





1 


9 


1 


1 


23 


10 


6 


15 


34 


1 


5 


2 





8 


2 





7 


3 


1 


6 


3 


11 


3 


13 


7 


3 


18 


35 





2 


8 





3 


7 


2 


1 


7 


1 


2 


7 


13 


9 


11 


13 


10 


12 


36 


1 


4 


5 





4 


6 


1 


4 


5 


1 


4 


5 


10 


8 


14 


17 


9 


8 


37 





3 


7 





2 


8 


1 


1 


8 





2 


8 


6 


5 


IS 


7 


5 


18 



Scoring of Results 23 



TABLE Ih 
Original Scores in Easy Opposites 









00 








CO 








m 








M 




-►^ 






t3 


y^-^ 






'T^ 


y"""^ 






-c 


^Ty 






T3 


^r^ 


xn 


1 


a 





+ 


6C 

s 


^3 


§ 

1X1 


+ 


g 


a 






+ 


bX) 

2 


73 
-(J 

a 


C 


CD 
W. 


+ 
IM 


(4-4 



^ 





0) 


« 


^ 





05 


P 


^ 








P 


^ 





a> 


9 


6 


6 


6 


6 


s 




6 


d 


s 


u 





6 


d 


a 







d 


d 


a 






^2; 


12? 


!z; 


H 


m 


!z; 


12; 


H 


m 


"i^ 


!2; 


H 


m 


"^ 


^ 


H 


m 


1 








16 


38 








19 


40 








18 


40 








25 


40 


2 








16 


39 








21 


40 








20 


39 








17 


40 


3 








24 


36 








35 


40 








30 


40 





1 


29 


38 


4 








20 


39 


1 





24 


38 








32 


40 








28 


40 


5 


2 





34 


36 








37 


40 


1 





31 


38 








34 


40 


6 


2 


2 


29 


31 


1 





31 


38 








27 


39 








33 


40 


7 








26 


39 








24 


40 








25 


40 








25 


40 


8 


H 





35 


37 








27 


40 


i 





28 


39 








29 


40 


9 





1 


27 


38 








23 


40 








25 


40 








24 


40 


10 


1 





36 


38 





1 


38 


38 








37 


40 


2 





36 


36 


11 


1 





22 


38 








23 


40 


1 


1 


29 


36 








23 


40 


12 


h 





28 


39 








35 


40 


1 





46 


38 








36 


40 


13 


1 





32 


38 


H 





32 


37 








21 


40 








24 


40 


14 


2 


1 


29 


32 





1 


29 


38 


h 





27 


39 





1 


35 


38 


15 


* 





25 


39 








21 


40 








28 


40 


1 





25 


38 


16 


* 





27 


39 


1 





25 


38 





2 


32 


36 


1 


1 


28 


36 


17 


i 





27i 


39 








36 


40 


* 





29 


39 








41 


40 


18 


2* 





47 


35 


2 





37 


36 


2h 





36 


35 


3 





40 


34 


19 


2^} 





39 


35 








33 


40 


0" 


1 


50 


40 


li 





37 


37 


20 


li 





43 


37 








49 


40 








41 


40 


1 





41 


38 


21 


2 





42 


36 








53 


40 








41 


40 





1 


79 


38 


22 


14 





46 


37 


i 


1 


53 


37 


Ih 


1 


54 


35 


li 


1 


48 


35 


23 





2 


32 


36 


2 





40 


36 








51 


40 


1 


1 


90 


36 


24 


7* 





32 


25 


4 





38 


32 


3* 


35 


33 


i 


5 


34 


29 


25 


2 


2 


60 


32 





2 


62 


36 


2| 


1 


58 


33 


n 


2 


49 


33 


26 


i 


2 


111 


35 


3 


3 


70 


28 


1* 


45 


37 








42 


40 


27 


1 





57 


38 








47 


40 


1" 





37 


38 


X 





38 


39 


28 


3 





32 


34 


2 





52 


36 


2 





33 


36 


2 





50 


36 


29 


2 





81 


36 


li 





82 


37 


+ 


1 


55 


37 


5:^ 





52 


29 


30 


4i 





54 


31 


2 





63 


36 


2* 





80 


35 


2 





76 


36 


31 


2i 


1 


80 


33 


3 


1 


57 


32 


3 


1 


115 


32 


2 


2 


75 


32 


32 


7 





40 


26 


2^ 


1 


47 


33 


H 





57 


29 


4i 


1 


82 


29 


33 


24 


6 


140 


23 


3 


5 


134 


24 


4-?r 


4 


150 


23 


11 


2 


132 


14 


34 


6 





77 


28 


5 





70 


30 


4 





72 


32 


1 





47 


38 


35 


4i 





80 


31 


9 





67 


22 


8 





76 


24 


1 





62 


38 


36 


9i 


4 


85 


13 


8 





81 


24 


4.\ 


1 


81 


29 


8J. 


3 


110 


17 


37 


8 


3 


205 


18 


6i 





115 


27 


13 





144 


14 


iii 





195 


17 



Score is 2 for each word right, plus 1 for each half right. 



24 Correlations of Mental Abilities 



TABLE li 
Original Scores in Hard Opposites 



1? 

1 


i-i 


CO 

6 


CO 

J2 


CO 

O 

m 


CO 
M 

>> 


CO 
d 

ID 


4-i 
Pf 


CO 


rH 

CO 




CO 

CO 


CO 


d 


o 
o 
m 


a 


o 
o 

m 


05 

a 


O 
o 

m 


1 


£ 
o 
o 


6> 

a 


O 
o 

m 


o 


o 

o 


o 
o 

m 


1 


55 


73 


55 


66 


55 


118 


51 


148 


65 


54 


66 


51 


2 


56 


84 


53 


67 


48 


121 


51 


133 


54 


52 


49 


44 


3 


56 


71 


50 


86 


62 


83 


63 


88 


49 


56 


47 


47 


4 


52 


71 


50 


81 


50 


109 


53 


112 


50 


50 


47 


50 


5 


52 


91 


46 


246 


54 


123 


51 


158 


49 


51 


61 


48 


6 


58 


116 


49 


161 


49 


119 


46 


162 


52 


49 


48 


41 


7 


52 


80 


54 


85 


48 


134 


52 


128 


51 


64 


40 


61 


8 


46 


128 


48 


152 


54 


149 


50 


137 


40 


48 


49 


49 


9 


53 


75 


50 


200 


51 


145 


61 


150 


49 


45 


46 


47 


10 


48 


140 


54 


156 


45 


172 


44 


165 


47 


53 


40 


48 


11 


47 


73 


46 


66 


48 


67 


48 


92 


47 


45 


39 


45 


12 


47 


94 


56 


152 


43 


141 


42 


198. 


45 


41 


41 


39 


13 


45 


109 


52 


166 


60 


135 


44 


196 


45 


49 


47 


41 


14 


46 


148 


53 


229 


38 


219 


42 


236 


47 


61 


35 


41 


15 


56 


62 


50 


79 


40 


123 


52 


69 


53 


49 


37 


49 


16 


35 


120 


50 


124 


33 


204 


45 


169 


35 


44 


27 


45 


17 


60 


184 


46 


215 


44 


189 


46 


184 


47 


47 


42 


48 


18 


41 


184 


43 


145 


24 


246 


24 


136 


37 


44 


22 


30 


19 


48 


286 


39 


190 


35 


341 


47 


234 


44 


38 


24 


44 


20 


48 


360 


50 


247 


40 


290 


61 


229 


46 


49 


39 


48 


21 


40 


350 


43 


236 


23 


373 


33 


238 


31 


40 


26 


33 


22 


29 


182 


31 


135 


18 


172 


19 


191 


25 


29 


16 


22 


23 


37 


230 


35 


190 


38 


304 


23 


290 


32 


34 


26 


24 


24 


21 


343 


28 


225 


17 


358 


19 


250 


19 


27 


12 


20 


25 


29 


192 


33 


198 


24 


171 


30 


209 


26 


36 


18 


27 


26 


40 


195 


35 


168 


26 


170 


29 


175 


40 


35 


17 


31 


27 


35 


190 


38 


203 


33 


201 


37 


236 


33 


34 


27 


34 


28 


42 


283 


35 


198 


30 


262 


31 


247 


38 


39 


24 


27 


29 


38 


398 


33 


310 


19 


365 


23 


250 


35 


32 


14 


21 


30 


18 


250 


16 


251 


12 


331 


17 


276 


13 


16 


12 


15 


31 


19 


341 


16 


256 


8 


215 


11 


220 


19 


14 


5 


17 


32 


17 


175 


29 


165 


12 


189 


9 


233 


15 


31 


10 


11 


33 


11 


370 


12 


451 














11 


12 








34 


6 


245 


23 


300 


7 


306 


10 


260 


4 


3 


6 


10 


35 


6 


250 


25 


225 


5 


220 


4 


248 


6 


26 


2 


7 


36 


18 


285 


23 


261 


10 


340 


9 


300 


14 


19 


5 


11 


37 


3 


136 





120 


2 


131 





141 


3 












Scoring of Results 



25 



TABLE li (cont'd) 

Original Scores in 
Hard Oppositbs 



TABLE Ij 

Original Scores in Ebbinghaus Test — 
Mutilated Text 















1— I 




(N 




CO 




T)H 




I— 1 


c<> 


fO 


Tj< 


1-1 


4J 


(N 


-i-i 


CO 


-hS 


Tj^ 


-jO 




+i 


-t^ 


•+-3 


+2 


-^^ 


S 


+i 


S 


-r= 


«2 


■ -^ 


m 


-i^ 


CO 


CQ 


m 


03 


CQ 





03 


Q 


tc 




Ul 


03 


u 


OJ 


OJ 


0) 


IB 


a> 


-U 


tt> 


-t-3 


<D 


"^ 





+i 


<D 


-^ 


-tJ 


->^ 


•t-s 


-^j 


-^ 


•+-I 


7* 


-tJ 


7^ 


-^ 


■v 


or-* 


^ 


„ 


.^ 


^ 


,^ 


ci 


^ 





^ 


« 


^ 


• 


-O 


xn 


m 


02 


CO 


02 


<u 


tc 


oJ 


m 


<D 


02 


0) 


;3 
xn 


>, 


>, 


>3 


>> 


t>i 


W 


t>» 


m 


>> 


m 


>> 


TO 




^ 


jn. 


XI 


J2 


^ 


.s 


X! 


.S 


^ 


G 


-Q 




"o 


a> 


<S3 


<a 


P 


0} 


<o 


CD 


« 


9 


03 


<o 




Q 


t4 















a 





s 





a 


u 



a 




































!2; 


m 


m 


02 


02 


02 


H 


02 


H 


02 


H 


m 


H 


1 


60 


60 


60 


56 


10 


40 


10 


31 


10 


39 


10 


47 


2 


58 


59 


53 


49 


9 


98 


10 


61 


8 


74 


9 


107 


3 


59 


58 


55 


52 


10 


37 


10 


53 


10 


50 


10 


53 


4 


58 


51 


54 


54 


9 


78 


9 


68 


8 


94 


9 


117 


5 


56 


55 


53 


54 


10 


91 


10 


90 


10 


83 


8 


S3 


6 


59 


49 


54 


52 


10 


101 


10 


93 


9 


77 


9 


106 


7 


55 


57 


53 


57 


10 


81 


10 


78 


10 


72 


9 


96 


8 


51 


53 


54 


53 


10 


125 


10 


67 


10 


65 


9 


197 


9 


59 


53 


57 


53 


10 


86 


10 


74 


10 


130 


9 


126 


10 


53 


54 


45 


49 


10 


81 


10 


61 


9 


105 


8 


216 


11 


54 


46 


51 


49 


10 


57 


10 


63 


9 


77 


9 


70 


12 


56 


45 


47 


40 


10 


57 


8 


110 


9 


104 


8 


96 


13 


58 


52 


54 


45 


10 


135 


10 


137 


10 


245 


10 


170 


14 


54 


51 


46 


45 


7 


136 


8 


74 


6 


161 


5 


138 


15 


58 


53 


40 


57 


9 


200 


10 


103 


10 


110 


9 


129 


16 


38 


49 


35 


50 


9 


88 


8 


93 


9 


92 


8 


94 


17 


54 


54 


55 


44 


9 


209 


9 


174 


9 


169 


8 


256 


18 


49 


50 


22 


29 


10 


85 


9 


307 


7 


120 


7 


134 


19 


51 


48 


39 


50 


9 


240 


7 


191 


7 


230 


7 


216 


20 


52 


49 


45 


52 


10 


290 


10 


189 


7 


425 


9 


372 


21 


39 


41 


26 


34 


5 


272 


7 


261 


5 


360 


3 


220 


22 


28 


37 


22 


25 


5 


195 


4 


170 


7 


159 


4 


199 


23 


46 


38 


36 


30 


7 


468 


7 


197 


4 


375 


4 


250 


24 


22 


27 


18 


18 


9 


217 


7 


360 


5 


275 


9 


154 


25 


34 


39 


24 


34 


10 


178 


10 


258 


8 


320 


7 


346 


26 


45 


39 


23 


33 


9 


172 


7 


200 


4 


206 


6 


256 


27 


42 


42 


39 


39 


8 


309 


7 


332 


5 


595 


9 


490 


28 


43 


40 


33 


30 


8 


205 


7 


198 


6 


220 


9 


320 


29 


42 


38 


18 


25 


8 


441 


7 


314 


9 


410 


4 


640 


30 


23 


19 


19 


21 


1 


502 


4 


369 


2 


405 


3 


430 


31 


19 


16 


7 


17 


3 


540 


3 


345 


3 


538 


6 


336 


32 


17 


34 


11 


13 


1 


250 


3 


205 


3 


245 


5 


318 


33 


11 


12 











240 

















34 


6 


25 


9 


12 





240 


3 


600 





360 


3 


395 


35 


10 


28 


7 


9 


2 


491 


6 


307 


2 


525 


1 


520 


36 


20 


22 


7 


15 


1 


466 


5 


384 


3 


540 


2 


489 


37 


3 





3 








210 





130 













26 



Correlations of Mental Abilities 



TABLE Ij (continued) 
Original Scores in Ebbinghaus Test — Mutilated Text 



o 


«3 

m 

-t-i 


(P 




CO 
03 






00 

03 


00 
-1^ 


15° 
6 


of 

(D 
U 
O 
O 
CO 


a 


o 
o 
CO 


d 

.s 
s 


co" 
>^ 

Si 

o 
o 


d 

CO 
CI 

tt) 

s 


of 

O 

CJ 

xn 


d 
<u 

S 
H 


1 


9 


42 


10 


82 


10 


50 


10 


52 


2 


9 


79 


9 


141 


8 


122 


9 


92 


3 


9 


46 


9 


74 


10 


60 


9 


80 


4 


9 


113 


8 


170 


7 


127 


10 


212 


5 


9 


92 


8 


106 


9 


140 


9 


110 


6 


7 


170 


8 


130 


8 


277 


9 


155 


7 


10 


152 


9 


278 


10 


139 


10 


84 


8 


9 


82 


9 


311 


10 


132 


9 


90 


9 


9 


108 


10 


176 


8 


268 


9 


92 


10 


8 


152 


8 


182 


7 


330 


9 


203 


11 


7 


88 


8 


91 


8 


85 


8 


117 


12 


9 


93 


8 


192 


5 


149 


8 


83 


13 


9 


163 


9 


315 


8 


258 


7 


397 


14 


9 


138 


7 


181 


7 


176 


9 


137 


15 


8 


108 


9 


205 


6 


213 


9 


396 


16 


6 


106 


5 


129 


5 


132 


9 


197 


17 


9 


124 


5 


257 


5 


313 


10 


208 


18 


9 


136 


5 


195 


6 


215 


8 


154 


19 


7 


182 


7 


307 


3 


291 


6 


209 


20 


9 


340 


4 


290 


6 


350 


10 


209 


21 


5 


341 


4 


316 


2 


286 





310 


22 


5 


251 


5 


220 


3 


217 


3 


207 


23 


6 


255 


4 


282 


3 


254 


3 


215 


24 


5 


284 


5 


265 


5 


227 


4 


266 


25 


7 


207 


3 


296 


5 


217 


5 


238 


26 


6 


364 


5 


331 


3 


204 


5 


177 


27 


4 


474 


6 


525 


7 


275 


3 


660 


28 


7 


218 


6 


328 


4 


303 


6 


221 


29 


9 


376 


3 


420 


5 


394 


4 


370 


30 


1 


390 


2 


310 


2 


259 





243 


31 


5 


302 


5 


320 


4 


412 


1 


426 


32 


3 


381 


3 


329 


3 


271 


2 


293 


33 






















34 


1 


480 


3 


270 


3 


478 


2 


450 


35 


4 


355 


4 


410 


2 


327 


2 


354 


36 


1 


140 


2 


403 


1 


270 


2 


265 


37 























Scoring of Results 



27 



TABLE Ij (continued) 
Original Scores in Ebbinghatjs Test — Mutilated Text 



Scores given by experimenter one 
month after 1st scoring by him (S2) 



Scores given by Miss R. 






I— 1 


(M 


CO 


'tJH 


K> 


CO 


t^ 


00 


r-l 


<M 


CO 


'>** 


"5 


CO 


i> 


00 


•2i 
-2 


to 

-(J 


m 



+3 




1 






-(J 


to 

<D 

+3 


+3 

<u 

-(J 




1 


-1^ 


+3 

CO 


+3 

CO 

(U 


1 


1 


w 


.s 


a 


.9 


_a 


.s 


a 


.s 


a 


a 





_g 


a 


a 


a 


a 


a 


6 


2 



CO 






U 




2 






i 





8 



u 


1 


i 


u 


2 




i 







1 

u 
03 


"i 



02 


£ 



1 


10 


10 


10 


10 


9 


10 


10 


10 


9 


10 


10 


10 


9 


10 


9 


10 


2 


10 


10 


9 


8 


9 


8 


7 


10 


9 


10 


9 


9 


9 


10 


8 


10 


3 


10 


10 


10 


10 


9 


10 


10 


9 


10 


10 


10 


10 


10 


10 


10 


9 


4 


9 


10 


8 


9 


9 


8 


8 


9 


10 


10 


9 


9 


10 


9 


8 


9 


5 


10 


10 


10 


9 


9 


8 


10 


9 


9 


10 


10 


10 


9 


8 


9 


9 


6 


10 


10 


9 


10 


8 


7 


8 


10 


10 


10 


9 


10 


9 


9 


9 


9 


7 


10 


10 


10 


9 


9 


10 


10 


10 


10 


10 


10 


9 


10 


9 


10 


10 


8 


10 


10 


10 


9 


9 


9 


10 


10 


10 


10 


10 


10 


10 


10 


10 


10 


9 


10 


10 


10 


9 


9 


10 


9 


9 


10 


10 


10 


10 


9 


10 


10 


9 


10 


10 


10 


9 


9 


7 


10 


8 


9 


10 


10 


9 


9 


8 


9 


8 


10 


11 


10 


9 


9 


10 


7 


8 


9 


7 


10 


9 


9 


10 


9 


9 


10 


8 


12 


10 


9 


9 


9 


9 


9 


8 


9 


10 


10 


9 


10 


10 


9 


9 


9 


13 


10 


10 


10 


9 


10 


9 


9 


9 


10 


10 


9 


9 


10 


9 


10 


9 


14 


8 


8 


7 


6 


9 


7 


8 


10 


9 


8 


7 


7 


9 


9 


9 


9 


15 


9 


10 


10 


10 


9 


9 


7 


10 


10 


10 


10 


10 


10 


8 


9 


9 


16 


10 


8 


9 


9 


7 


7 


7 


9 


9 


8 


9 


9 


8 


8 


8 


9 


17 


10 


9 


9 


9 


9 


6 


5 


10 


10 


9 


9 


9 


10 


9 


7 


10 


18 


10 


9 


8 


5 


9 


5 


7 


8 


10 


10 


8 


9 


9 


7 


9 


9 


19 


9 


8 


9 


9 


9 


6 


6 


7 


9 


8 


9 


8 


9 


8 


7 


8 


20 


10 


10 


7 


9 


9 


4 


5 


10 


9 


10 


7 


9 


9 


4 


9 


10 


21 


7 


6 


6 


4 


7 


5 


3 





6 


7 


8 


5 


8 


6 


6 


1 


22 


7 


6 


7 


5 


6 


6 


2 


4 


8 


8 


8 


7 


8 


7 


8 


7 


23 


6 


6 


4 


4 


4 


4 


4 


3 


6 


8 


6 


5 


8 


5 


7 


4 


24 


9 


8 


5 


9 


7 


6 


5 


7 


9 


8 


7 


10 


7 


6 


6 


7 


25 


10 


9 


9 


7 


7 


2 


4 


4 


10 


10 


9 


8 


9 


7 


6 


4 


26 


9 


7 


2 


7 


5 


6 


3 


6 


9 


8 


5 


8 


8 


8 


6 


7 


27 


8 


6 


8 


9 


2 


4 


4 


3 


9 


8 


7 


9 


7 


7 


9 


6 


28 


9 


8 


7 


8 


8 


4 


5 


7 


9 


8 


7 


9 


9 


8 


8 


7 


29 


8 


7 


8 


3 


9 


3 


5 


5 


8 


8 


9 


6 


3 


10 


4 


5 


30 


1 


5 


1 


2 





1 


1 





2 


4 


3 


2 


3 


4 


3 


3 


31 


5 


3 


3 


5 


6 


4 


3 


3 


7 


7 


6 


7 


9 


6 


5 


5 


32 


2 


4 


3 


5 


3 


1 


1 





4 


4 


3 


4 


4 


4 


4 


3 


33 


















































34 





2 


1 


1 





3 


1 


1 





7 


3 


5 


5 


6 


6 


5 


35 


2 


3 


1 


2 


1 


2 





3 


4 


7 


3 


4 


4 


4 


6 


4 


36 


1 


3 


3 


2 


1 


1 


1 


1 


2 


7 


4 


5 


3 


3 


4 


3 


37 



















































28 



Correlations of Mental Abilities 



TABLE Ik 

Original Scores in 
Scroll 



TABLE n TABLE Im 

Original Scores 

IN Drawing Original Scores in Esti- 
Lengths mating Lengths 





o 


8 

.S 
0) 


O 


T3 

a 
o 
o 

0) 

.S 

01 


s 

o 

i 

o 

'■^'^ 
.3 ^ 

(33 T3 

e 

OQ 


"3 

GO 
i-H 

CO 

a 
o 

1 


"3 

a 
o 


H 
CO 
o 

.2 


Times Correct 


in 


8 Trials 




First Trial 


Second Trial 


"8 

a> 

1 


s 
s 

o 

o 

I-H 


a 

o 
o 

r-l 


S 
S 

o 

o 

l—f 


s 
a 

o 
o 

1— ( 


i 

o 
o 
1— t 


a 
a 

o 
o 

I— 1 


a a 
a a 

o o 
o o 

I-H I-H 


o 


6 




d 




u 

> 


> 




o 

I-H 


CD 
O 


1 

o 

T-H 


§ 


I— 1 


CO 
o 

I-H 


O O 

I-H I— ( 


1 


3 


347 


16 


184 


35 


9 


14 


12 


8 


8 


8 


7 


8 


8 


8 8 


2 


31 


102 


22 


125 


63 


21 


24 


18 


7 


8 


7 


4 


8 


8 


7 7 


3 


10 


241 


12 


242 


18 


11 


4 


3 


8 


8 


8 


6 


8 


8 


8 8 


4 


4 


440 


13 


155 


68 


41 


16 


11 


8 


8 


8 


8 


8 


8 


8 6 


5 


23 


128 


6 


137 


25 


8 


12 


5 


8 


8 


8 


8 


8 


8 


8 8 


6 


52 


136 


15 


170 


17 


3 


9 


5 


8 


8 


7 


4 


8 


8 


8 6 


7 


25 


136 


18 


163 


20 


5 


10 


5 


7 


8 


7 


6 


8 


8 


7 4 


8 


17 


217 


24 


188 


56 


15 


21 


20 


8 


8 


7 


5 


8 


8 


8 5 


9 





340 


18 


142 


17 


5 


4 


8 


8 


8 


8 


8 


8 


8 


8 8 


10 


28 


110 


15 


145 


29 


7 


11 


11 


8 


8 


8 


7 


8 


8 


8 6 


11 


22 


186 


17 


151 


38 


10 


20 


8 


8 


8 


7 


7 


8 


8 


7 6 


12 


5 


207 


12 


151 


94 


26 


35 


33 


8 


8 


8 


5 


8 


8 


8 8 


13 


30 


83 


26 


97 


11 


6 


4 


1 


8 


8 


8 


6 


8 


8 


8 6 


14 


39 


94 


18 


119 


36 


8 


14 


14 


8 


8 


7 


8 


8 


8 


8 8 


15 


10 


219 


22 


123 


35 


12 


15 


8 


8 


8 


8 


8 


8 


8 


8 8 


16 


30 


103 


58 


97 


37 


10 


11 


16 


8 


8 


8 


6 


8 


8 


8 8 


17 


5 


287 


36 


155 


26 


8 


9 


9 


8 


8 


7 


5 


8 


8 


7 6 


18 


42 


172 


37 


123 


101 


33 


35 


23 


7 


8 


7 


6 


8 


8 


7 6 


19 


34 


380 


62 


130 


13 


2 


5 


6 


7 


8 


7 


6 


8 


7 


6 6 


20 


7 


367 


30 


232 


30 


13 


11 


6 


8 


8 


8 


6 


8 


8 


8 5 


21 


13 


425 


42 


184 


56 


15 


22 


19 


8 


7 


5 


5 


8 


8 


7 5 


22 


18 


271 


30 


156 


70 


17 


20 


33 


8 


7 


5 


5 


8 


8 


7 5 


23 


33 


460 


54 


168 


104 


41 


34 


29 


8 


8 


7 


4 


8 


8 


8 7 


24 


21 


144 


26 


147 


32 


11 


8 


13 


8 


4 


8 


7 


8 


8 


7 7 


25 


20 


229 


50 


100 


42 


19 


6 


17 


8 


8 


5 


6 


8 


8 


2 5 


26 


49 


100 


54 


137 


18 


5 


5 


8 


8 


8 


7 


6 


8 


8 


7 7 


27 


84 


212 


126 


150 


22 


10 


7 


5 


8 


8 


8 


8 


8 


8 


6 5 


28 


12 


279 


21 


140 


23 


9 


7 


7 


7 


5 


5 


4 


7 


5 


4 4 


29 


108 


107 


60 


155 


25 


4 


10 


11 


5 


7 


6 


5 


8 


S 


5 7 


30 


68 


217 


48 


152 


22 


13 


5 


4 


8 


8 


8 


6 


8 


8 


8 6 


31 


64 


147 


67 


184 


46 


9 


12 


25 


8 


8 


8 


8 


8 


8 


8 5 


32 


75 


230 


82 


175 


125 


39 


47 


39 


7 


6 


6 


6 


7 


4 


5 7 


33 


20 


200 


32 


178 


47 


16 


22 


9 


8 


8 


6 


5 


8 


8 


6 3 


34 


6 


405 


4 


430 


25 


7 


12 


6 


5 


8 


8 


7 


8 


8 


8 6 


35 


18 


501 


36 


151 


28 


3 


14 


11 


8 


7 


7 


7 


7 


8 


6 5 


36 


72 


155 


34 


221 


32 


6 


15 


11 


8 


8 


8 


7 


8 


8 


8 8 


37 


23 


500 


33 


283 


108 


40 


61 


67 


8 


7 


5 


5 


8 


8 


6 5 



Scoring of Results 



29 



TABLE In 
Original Scores in Completing Words — BA Test 





IB 

'2 
m 


6 




1-1 

2 
6 


1—1 

m 

a 


6 


1—1 
ai 

6 

B 

a 


1 

6 


1 

d 


<s 

-t-i 

a 


i 


m 

.s 
a 


CO 

1 
1 

1 


CO 
<S 

bh 
a 



CO 

tT 
a> 
-fj 

a 


6 


CO 

.a 
a 


1 

1 

6 


-u 
m 
<0 
-1-2 

bio 

a 
g 

1 


-a 

a 


6 




a 


1 


30 








46 


30 








46 


30 








195* 


30 








144 


2 


30 








50 


30 








72 


29 


1 





126 


30 








108 


3 


30 








57 


30 








64 


28 


2 





69 


27 





3 


95 


4 


30 








79 


30 








54 


30 








103 


30 








170 


5 


30 








65 


30 








75 


29 


1 





97 


30 








134 


6 


30 








57 


30 








46 


29 





1 


128 


30 








89 


7 


30 








99 


30 








95 


30 








131 


30 


1 


1 


169 


8 


30 








87 


30 








57 


29 





1 


121 


26 





4 


241 


9 


30 








62 


30 








48 


30 








100 


30 








111 


10 


30 








138 


30 








75 


-30 








125 


30 








164 


11 


30 








93 


30 








65 


29 


1 





132 


29 





1 


235 


12 


28 


1 


1 


71 


30 








64 


29 





1 


70 


30 








124 


13 


30 








71 


30 








71 


28 





2 


97 


30 








97 


14 


30 








70 


27 


1 


2 


97 


30 








94 


26 


1 


3 


96 


15 


30 








54 


28 


2 





57 


29 





1 


126 


28 





2 


195 


16 


30 








68 


30 








96 


30 








110 


28 





2 


130 


17 


30 








146 


30 








90 


28 





2 


110 


30 








111 


18 


30 








90 


30 








77 


25 


5 





95 


28 


2 





124 


19 


30 








166 


30 








108 


30 








124 


29 





1 


185 


20 


30 








146 


30 








155 


28 


2 





212 


28 


1 


1 


285 


21 


30 








217 


30 








177 


28 


2 





232 


24 


4 


2 


213 


22 


26 


4 





96 


23 


6 


1 


125 


17 


7 


6 


184 


18 


6 


6 


204 


23 


28 


2 





322 


30 








190 


30 








366 


27 


2 


1 


300 


24 


30 








68 


30 








64 


29 





1 


147 


23 


3 


4 


148 


25 


30 








164 


30 








160 


















26 


28 





2 


166 


29 





1 


145 


22 





8 


187 










27 


30 








246 


26 


1 


3 


340 


29 





1 


268 


30 








256 


28 


29 


1 





102 


30 








83 


26 


1 


3 


260 


28 





2 


212 


29 


24 


5 


1 


222 


27 


3 





194 


28 


2 





262 


21 


2 


7 


336 


30 


28 


2 





190 


30 








205 


17 


3 





465 


21 


4 


5 


490 


31 


24 


6 





177 


17 


13 





160 


14 


8 


8 


202 


14 


4 


12 


244 


32 


22 


8 





137 


23 


7 





166 


20 


9 


1 


172 


17 


12 


1 


171 


33 


19 


10 


1 


290 








30 




















34 


30 








390 


29 


1 





390 


21 


1 


8 


451 


19 





11 


451 


35 


30 








247 


30 








247 


25 


1 


4 


394 


30 








362 


36 


26 


4 





221 


28 


2 





180 


15 


7 


8 


482 


18 


5 


7 


455 


37 


15 


4 


11 


222 


16 


1 


13 


205 


1 





29 


200 


1 


1 


28 


130 



*2 min. 5 sec. lost oa last word. 



Correlations of Mental Abilities 



TABLE II 
Total Scores, and Scores in 1st and 2nd Trials 



xn 



P^ Ph 






O 
O 

a 

a; 



>■ 



C3 



1 

2 
3 
4 
5 

6 

7 

8 

9 

10 

11 
12 
13 
14 
15 

16 
17 

18 
19 
20 
21 
22 

23 
24 
25 
26 
27 

28 
29 
30 
31 
32 



73| 36i 

78 37^ 

69^ 30i 

76i 351 

77J 37i 

71 1 30i 

64J 33 

58i 26i 

591 28 

661 31i 



69 
701 



39^ 
35i 



43^ 21i 

461 2H 

28i 101 

50 23J 
69i 31i 

44* 18 

38i 20 

52i 23i 

51 24J 
17* 8 

43i 19^ 

40 17i 

23i 11 

341 14i 



37^ 37 

40^ 34 

38| 38 

40i 36 

40 28 

41 i 38 
31J 25 
3U 25 
31i 36 
35i 27 

29i 26 

35J 29 

22\ 27 

25i 23 

18 29 

26J 31 

38 23 

26i 23 

18i 19 

29 25 

26i 21 

9i 21 

231 27 

22| 20 

12i 19 

20J 18 



18 
20 
18 
19 
15 



19 
14 
20 
17 
13 



18 20 
11 14 



11 
17 
13 



14 
19 
14 



13 13 
16 13 

14 13 

10 13 

11 18 

16 15 

11 12 



12 

8 

13 

11 

11 



11 
11 
12 
10 
10 



21| lOi \\\ 17 



2\\ 11 

23 12 

29i 161 

14 6i 



10^ 20 

11 17 

12| 19 

1\ 16 



I 2\\ 13 8i 17 



15 12 

11 9 

11 8 

8 10 

9 6 



12 
9 
9 

10 



256 
237 
280 
260 
264 

258 
314 
261 
314 
220 

213 
280 
194 
268 
255 

297 
299 

225 
254 
377 

381 
237 

398 
315 
349 
304 
359 



121 135 

100 137 

114 166 

121 139 

122 142 

126 132 

166 148 

118 143 

144 170 

100 120 

98 115 

133 147 

92 102 

126 142 

132 123 

139 158 

148 151 

118 117 

125 129 

162 215 

236 145 

137 100 

197 201 

136 179 

189 160 

157 147 

180 179 



97 
157 
195 
203 
209 

225 
241 
121 
227 
186 

165 
178 
200 
239 
176 

293 
262 

170 
168 
363 
518 
308 

350 
240 
210 
346 

287 



54 

85 



43 

72 



90 105 



92 
109 



111 
91 



131 94 

111 130 

58 63 

116 111 

92 94 



101 

95 

101 



64 
83 
99 



105 134 

92 84 

146 147 

126 136 

74 96 

70 98 

153 210 

262 256 

134 174 

181 1G9 

105 185 

107 103 

175 171 

131 156 



8 


352 


177 


175 


307 


167 


140 


8 


373 


212 


161 


215 


105 


110 


10 


372 


198 


174 


566 


229 


337 


6 


383 


215 


168 


485 


231 


254 


9 


345 


172 


173 


330 


158 


172 



33 


12| 


6 


61 


14 


7 


7 


452 


287 


165 


302 


137 


165 


34 


231 


17J 


6 


14 


9 


5 


502 


270 


232 


546 


273 


273 


35 











8 


1 


7 


588 


278 


310 


310 


159 


151 


36 


15 


5J 


n 


18 


9 


9 


2S9 


145 


144 


632 


307 


325 


37 


41 


3i 


u 


12 


8 


4 


4G0 


272 


188 


533 


226 


307 



Scoring of Results 



31 



TABLE II (continued) 

Total Scores, and Scores in 1st and 2nd Trials 







-+J 


T3 


m 


m 






-t^ 






cc 


-0 






CO 

r-l 




g 


a 


S 




i-H 


C<) 




I-H 


(M 






,^ 


■^ 











CO 


XCl 


aT 


tn 


?r 


x£ 


-8 


S 


m 


S 


\^ 


fS 


fr^ 




<» 


03 



^ 






OJ 


■rf 


■3 


'S 


bC 


bC 


bC 


'CQ 


"m 


"m 


'm 


'm 


'S 




P. 


PL| 


Ph 


.5 


.S ' 


.S 









ft 



ft 



ft 



ft 


'3 




6C 


'5 

■pi 




'S 
bfl 



's 

'3 




0. 



>1 




&( 

f^ 


ft 

'2 


ft 


ft 

13 




3 


c3 


c^ 











m 


m 


m 


M 


53 


^ 


d 


CD 


OJ 


Oi 


03 


03 


cu 


03 


03 


a 


03 


c3 


(73 


^ 


^ 


vS 


h:^ 


P^ 


Pi 


rt 


w 


w 


H 


w 


w 


W 


1 


15 


5 


10 


27 


16 


11 


82 


39 


43 


617 


223 


394 


2 


24 


12 


12 


19 


17 


2 


78 


39 


39 


781 


263 


518 


3 


38 


19 


19 


24 


15 


9 


130 


67 


63 


672 


285 


387 


4 


23 


8 


15 


21 


10 


11 


110 


50 


60 


777 


348 


429 


5 


37 


17 


20 


25 


15 


10 


148 


79 


69 


1018 


541 


477 


6 


iSi 


74 


11 


23 


12 


11 


144 


82 


62 


1014 


453 


561 


7 


7 


5 


2 


20 


9 


11 


102 


52 


50 


811 


313 


498 


8 


29 


11 


18 


21 


9 


12 


127 


68 


59 


1066 


576 


490 


9 


30 


13 


17 


22 


13 


9 


103 


54 


49 


994 


479 


515 


10 


10 


4 


6 


18 


10 


8 


163 


82 


81 


1193 


500 


693 


11 


11 


5 


6 


25 


17 


8 


109 


49 


60 


918 


439 


479 


12 


30 


13 


17 


13 


8 


5 


151 


65 


86 


1297 


526 


771 


13 


24 


8 


16 


24 


9 


15 


119 


74 


45 


1158 


507 


651 


14 


13 


6 


7 


20 


8 


12 


146 


78 


68 


1516 


609 


907 


15 


30+ 


12i 


18 


16 


5 


11 


105 


48 


57 


837 


305 


532 


16 


24i 


12 


12i 


24 


15 


9 


134 


58 


76 


1543 


680 


863 


17 


13 


6 


7 


16 


7 


9 


137 


65 


72 


1344 


647 


697 


18 


8 


4 


4 


11 


5 


6 


200 


102 


98 


1931 


713 


1218 


19 


7 


3 


4 


12 


9 


3 


175 


82 


93 


1903 


844 


1059 


20 


3 


2 


1 


3 


4 


— 1 


184 


98 


86 


1730 


871 


859 


21 


5 


3 


2 


9 


6 


3 


227 


103 


124 


2441 


1090 


1351 


22 


10 


3 


7 


15 


12 


3 


233 


111 


122 


2356 


1041 


1315 


23 


5i 


3* 


2 


7 





7 


237 


88 


149 


2298 


972 


1326 


24 


4 


2 


2 


10 


6 


4 


221 


116 


105 


3064 


1432 


1632 


25 


10 


4 


6 


—4 


—5 


1 


279 


146 


133 


2234 


1042 


1192 


26 


5 


2.V 


2 


10 


2 


8 


328 


235 


93 


2016 


867 


1149 


27 


10 


4 


6 


9 


5 


4 


189 


108 


81 


1978 


937 


1041 


28 


2 


1 


1 


9 


9 





203 


104- 


99 


2122 


873 


1249 


29 


6 


3 


3 


14 


4 


10 


312 


177 


135 


2851 


1276 


1575 


30 


3+ 


3 


i 


2 


2 





317 


143 


174 


3184 


1521 


1663 


31 


9" 


4 


5 


12 


3 


9 


389 


167 


222 


3240 


1625 


1615 


32 


2 





2 


4 


4 





312 


129 


183 


2806 


1208 


1598 


33 


1 


1 





4 





4 


708 


340 


368 


4040 


1985 


2055 


34 


2 


1 


1 


12 


8 


4 


320 


191 


139 


3427 


1637 


1790 


35 


3 





3 


7 


4 


3 


375 


201 


174 


3287 


1515 


1772 


36 


3 


1 


2 


10 


2 


8 


521 


252 


269 


3374 


1522 


1852 


37 


1 





1 


3 


1 


2 


837 


390 


447 


3402 


1710 


1692 



32 



Correlations of Mental Abilities 



TABLE II (continued) 
Total Scores, and Scores in 1st and 2nd Trials 







■s 












1— 1 


T3 






1-H 


a 






r-l 


(M 








03 


oT 


m' 




"^ 


— 




-!-:> 


-Ij" 


-ij' 










g 


s 






CO 




0) 


<o 


li 








o 


o 


O 


o 


o 


o 




H 


H 


H 








N 


f^ 


P^ 


^ 


^ 


rs 


CO 

o 




1 


to 

1 




1— 1 


13 
C 


'B 


"3 


"3 
g 


.S 

ID 


M 

(V 




o" 


S 
^ 


IB 

J2 


IS 

X! 


1 


1 


1 


8 


o 


o 


a 

o 


a 

o 


a 

o 


^ 


H 


w 


W 


cc 


cc 


CO 


o 


O 


O 


O 


O 


O 


1 


761 


326 


435 


71 


37 


34 


164 


81 


83 


92 


46 


46 


2 


475 


224 


251 


75 


41 


34 


104 


53 


51 


122 


50 


72 


3 


678 


307 


371 


70 


34 


36 


162 


80 


82 


121 


57 


64 


4 


394 


166 


228 


76 


48 


28 


205 


111 


94 


133 


79 


54 


5 


472 


222 


250 


54 

7 
92 


35 


19 


200 


112 


88 


140 


65 


75 


6 


397 


176 


221 


65 


32 


164 


86 


78 


103 


57 


46 


7 


438 


185 


253 


70 


38 


34 


192 


98 


94 


194 


99 


95 


8 


421 


198 


223 


76 


38 


42 


194 


116 


78 


144 


87 


57 


9 


418 


191 


227 


68 


34 


32 


178 


95 


83 


110 


62 


48 


10 


364 


165 


199 


6 


39 


29 


145 


75 


70 


213 


138 


75 


11 


524 


241 


283 


72 


40 


32 


163 


88 


75 


158 


93 


65 


12 


440 


204 


236 


52 


25 


27 


224 


118 


106 


155 


91 


64 


13 


334 


158 


176 


73 


38 


35 


132 


62 


70 


147 


71 


71 


14 


363 


163 


200 


77 


48 


29 


135 


79 


56 


197 


70 


127 


15 


351 


163 


188 


65 


31 


34 


152 


67 


85 


131 


54 


77 


16 


408 


188 


220 


107 


40 


67 


178 


92 


86 


164 


68 


96 


17 


326 


164 


162 


84 


33 


51 


182 


90 


92 


236 


146 


90 


18 


342 


173 


169 


108 


59 


49 


203 


100 


103 


167 


90 


77 


19 


289 


150 


138 


147 


72 


75 


192 


98 


94 


274 


166 


108 


20 


277 


149 


128 


96 


43 


53 


273 


122 


151 


301 


146 


155 


21 


200 


118 


83 


130 


55 


75 


178 


01 


87 


394 


217 


177 


22 


264 


131 


133 


90 


45 


45 


186 


104 


82 








23 


208 


115 


93 


149 


79 


70 


338 


176 


162 


532 


342 


190 


24 


263 


143 


120 


75 


35 


40 


222 


120 


102 


132 


68 


64 


25 


269 


158 


111 


102 


42 


60 


236 


128 


108 


324 


164 


160 


26 


259 


131 


128 


126 


59 


67 


238 


110 


128 


341 


186 


155 


27 


209 


118 


91 


246 


105 


141 


233 


128 


105 








28 


275 


141 


134 


74 


39 


35 


265 


122 


143 


195 


112 


83 


29 


209 


116 


93 


193 


118 


75 


184 


108 


76 








30 


119 


70 


49 


152 


89 


63 


232 


119 


113 


415 


210 


205 


31 


176 


92 


84 


163 


78 


85 


303 


162 


141 








32 


159 


99 


60 


197 


98 


99 


220 


118 


102 








33 











89 


40 


49 


239 


131 


108 








34 


122 


54 


68 


93 


46 


47 


281 


164 


117 


790 


390 


400 


35 


134 


71 


63 


119 


68 


51 


603 


312 


291 


494 


247 


247 


36 . 


128 


80 


47 


143 


87 


56 


240 


149 


91 








37 











134 


73 


61 


326 


157 


169 









Scoring of Results 



33 



TABLE II (continued) 
Total Scores, and Scores in 1st and 2nd Trials 













-g 








.o 


t3 




i-i 


(N 






m 


a 




^ 


^ 






rH 


IM 


m 

Xi 


CO 


CO 






do" 




t 


-So 




o 

ID 


^ 


« 


a 


^ 


^ 


^ 


3 


^ 


^ 


^ 




s 


.s 


m 


s° 


tc 


bo 


'-+3 


-f^ 


%^ 




c 


a 


a 


a 


03 


d 


"o 


'% 


'^ 


■? 


B 


B 


B 




F 


P 


§ 


'-3 


■^ 


*-4-» 


o 


!h 


(h 


%^ 


XD 


m 


CC 


)^ 


P 


Q 


Q 


W 


W 


W 


1 


35 


17 


15 


63 


31 


32 


2 


63 


28 


32 


56 


26 


30 


3 


18 


8 


9 


62 


30 


32 


4 


68 


28 


39 


62 


32 


30 


5 


25 


10 


14 


64 


32 


32 


6 


17 


11 


6 


57 


27 


30 


7 


20 


5 


12 


55 


28 


27 


8 


56 


18 


29 


57 


28 


29 


9 


17 


5 


9 


64 


32 


32 


10 


29 


11 


13 


61 


31 


30 


11 


38 


10 


25 


59 


30 


29 


12 


94 


44 


45 


61 


29 


32 


13 


11 


6 


5 


59 


30 


29 


14 


36 


15 


17 


63 


31 


32 


15 


35 


18 


14 


64 


32 


32 


16 


37 


15 


16 


62 


30 


32 


17 


26 


10 


10 


57 


28 


29 


18 


101 


55 


44 


55 


28 


27 


19 


13 


4 


8 


61 


30 


31 


20 


30 


23 


5 


59 


30 


29 


21 


56 


26 


23 


61 


30 


31 


22 


70 


28 


24 


53 


25 


28 


23 


104 


55 


47 


58 


27 


31 


24 


32 


21 


9 


57 


27 


30 


25 


42 


23 


17 


50 


27 


23 


26 


18 


5 


13 


59 


29 


30 


27 


22 


6 


14 


59 


32 


27 


28 


23 


10 


11 


41 


21 


20 


29 


25 


18 


7 


51 


23 


28 


30 


22 


13 


8 


60 


30 


30 


31 


46 


16 


22 


61 


32 


29 


32 


125 


57 


57 


48 


25 


23 


33 


47 


19 


26 


52 


27 


25 


34 


25 


13 


11 


58 


28 


30 


35 


28 


15 


10 


55 


29 


26 


36 


32 


8 


18 


63 


31 


32 


37 


168 


61 


84 


52 


25 


27 



34 



Correlations of Mental Abilities 



TABLE III 
Rank of Subjects in the Different Tests 

















































































m 










to 


03 


M 




+5 




fcO 
a 
m 

o 


o 

t 

o 


+i 




"S, 

p-( 


a 
a 


"m 
O 


to 
<» 

'm 
O 
P. 


m 

(A 




S 
o 


in 

o 


"5) 

ID 


"So 

C 

o 


m 
o 


m 

t4-4 
O 


o 


o 




W3 


ho 

1 


o 

CI 


O 
>> 


Oh 

o 


fcX) 

3 


■g 


-4J 

g 

o 




g 


1 


6 


bC 


<u 


l2 


< 


TJ 


<D 


CD 


-as 


d 


XX 


O 


a> 


o 


to 


?:; 


fe 


< 


^ 


s 




< 


hJ 


p;' 


W 


W 


H 


CO 


a 


a 


td 


Q 


1 


34 


4 


3 


9 


1 


12 


1 


2 


1 


1 


8 


8 


1 


6 


20 


2 


29 


1 


6 


5 


3 


8 


13 


1 


4 


5 


13 


1 


5 


31 


30 


3 


28 


7 


1 


15 


10 


1 


5 


10 


2 


2 


6 


6 


4 


9^ 


5 


4 


28 


3 


4 


11 


13 


10 


9 


7 


3 


10 


15 


21 


8 


9Jt 


31 


5 


36 


2 


10 


13 


11 


2 


2 


15 


10 


6 


2 


19 


9 


2| 


12 


6 


24 


5 


1 


10 


16 


11 


7 


13 


9 


12 


22 


8 


2 


29 


3 


7 


25 


11 


16 


21 


20 


22 


11 


3 


5 


9 


9 


16 


16 


29 


7 


8 


29 


13 


16 


12 


2 


6 


9 


9 


11 


11 


6 


18 


10 


29 


28 


9 


35 


12 


4 


21 


17 


4 


8 


4 


8 


7 


4 


11 


3 


2* 


3 


10 


36 


10 


12 


3 


9 


17 


14 


17 


13 


14 


5 


4 


19 


16 


16 


11 


30 


9 


14 


2 


4 


15 


2 


6 


7 


3 


9 


7 


13 


16 


24 


12 


29 


6 


8 


15 


8 


4 


19 


16 


14 


4 


1 


24 


12 


16 


34 


13 


32 


19 


12 


1 


11 


8 


5 


8 


2 


13 


11 


2 


11 


25^ 


1 


14 


35 


17 


19 


14 


18 


13 


11 


14 


16 


15 


16 


3 


IS 


2\ 


22 


15 


24 


25 


8 


8 


7 


3 


15 


5 


6 


17 


3 


5 


7 


2i 


20 


16 


24 


16 


7 


18 


23 


7 


5 


11 


17 


8 


24 


11 


14 


9i 


23 


17 


35 


7 


19 


19 


21 


13 


15 


12 


15 


18 


17 


13 


20 


2b\ 


14 


18 


31 


18 


19 


4 


6 


21 


23 


21 


20 


16 


25 


20 


15 


22 


33 


19 


40 


22 


26 


7 


5 


22 


21 


18 


19 


19 


31 


16 


21 


16 




20 


30 


14 


16 


30 


31 


31 


34 


19 


18 


21 


21 


32 


22 


25^ 


17 


21 


31 


15 


21 


31 


33 


26 


28 


24 


27 


29 


28 


11 


25 


6 


28 


22 


23 


32 


21 


5 


26 


17 


17 


25 


26 


23 


19 


15 




34 


32 


23 


45 


20 


12 


33 


30 


25 


30 


26 


25 


26 


32 


36 


28 


25i 


35 


24 


25 


21 


23 


23 


19 


28 


25 


23 


30 


24 


13 


23 


6 


9i 


18 


25 


36 


27 


26 


25 


14 


17 


37 


27 


24 


22 


22 


27 


23 


33 


25 


26 


38 


23 


28 


20 


29 


26 


25 


32 


22 


25 


27 


28 


24 


16 


6 


27 


43 


29 


33 


27 


22 


17 


28 


20 


21 


27 


37 


26 




16 


8 


28 


38 


30 


23 


26 


25 


34 


28 


22 


23 


20 


12 


31 


17 


37 


10 


29 


30 


28 


30 


29 


15 


24 


18 


28 


29 


27 


35 


14 




32 


12 


30 


52 


24 


26 


28 


36 


29 


36 


30 


31 


34 


33 


25 


26 


22 


8 


31 


23 


34 


32 


32 


32 


20 


21 


34 


32 


30 


34 


34 




16 


26 


32 


35 


31 


30 


24 


28 


34 


32 


28 


28 


31 


36 


22 




16 


36 


33 


39 


35 


34 


34 


24 


36 


32 


36 


37 


36 


18 


29 




36 


27 


34 


41 


26 


34 


36 


35 


34 


21 


31 


36 


35 


20 


33 


29 


16 


12 


35 


60 


37 


37 


37 


27 


31 


30 


33 


33 


33 


26 


37 


27 


22 


15 


36 


36 


33 


28 


17 


37 


31 


25 


35 


34 


32 


30 


30 




6 


18 


37 


24 


36 


36 


35 


34 


36 


34 


37 


35 


36 


29 


35 




35 


37 



The Reliability of the Tests 3 5 

V. The Reliability of the Tests 

I, The two different methods used in treating correlation data. 

In all the discussions of correlations two different methods 
are used. First : Each measure is used in the form of a devia- 
tion, plus or minus, from the central tendency of the Good group 
in that trait, or of the Poor group if the individual in question 
belongs to that group. The coefficients of correlation so ob- 
tained measure the relation between (i) an individual's devia- 
tion in one test from the median of his group (the Good or the 
Poor) in that test and (2) his deviation in some other test from 
the median of his group in that other test. Second: Each 
measure is used in the form of a deviation, plus or minus, 
from the median of the entire thirty-seven individuals in that 
test. This median is approximately the central tendency for 
adult men the country over in the trait in question, since the 
Good and Poor represent, in tests correlated with intelligence, 
a group of seventeen cases far above that central tendency, and 
a group of twenty cases probably not quite so far below that 
central tendency. The coefficients of correlation by the second 
method then represent approximately the relation between (i) 
an individual's deviation in one test from the central tendency 
of all adults in that test, and (2) his similar deviation in another 
test, — but in the case not of a random group but of a group 
chosen from, say, the top and bottom ten per cent for general 
intelligence. 

This difference is illustrated in the case of the A test and 
Geometrical Forms test by the table following : 



36 



Correlations of Mental Abilities 



TABLE IV 











Deviation from 




Score in 
A 


Score in 
Geometrical 


Deviation from 

Median of 

Good Group 


Median of Both 
Groups Combined, 

(i.e., approximate 
central tendency 


1 


test 


Forms 




for people in general) 




A Geometrical 


A Geometrical 


m 






test Forms 


test Forms 


1 


256 


164 


5 





43 


36 


2 


237 


104 


24 


60 


62 


96 


3 


280 


162 


—19 


2 


19 


38 


4 


260 


205 


1 


—41 


39 


—5 


5 


264 


200 


—3 


—36 


35 





6 


258 


164 


3 





41 


36 


7 


314 


192 


—53 


—28 


—15 


8 


8 


261 


194 





—30 


38 


6 


9 


314 


178 


—53 


—14 


—15 


22 


10 


220 


145 


41 


19 


79 


55 


11 


213 


163 


48 


1 


86 


37 


12 


280 


224 


—19 


—60 


19 


—24 


13 


194 


132 


67 


32 


105 


68 


14 


268 


135 


—7 


29 


31 


65 


15 


255 


152 


6 


12 


44 


48 


16 


297 


178 


—36 


—14 


2 


22 


17 


299 


182 


—38 


—18 





18 




Deviation from 










Median of 








225 


203 


Poor Group 


74 




18 


141 


34 


—3 


19 


254 


192 


112 


45 


45 


8 


20 


377 


273 


—11 


—36 


—78 


—73 


21 


381 


178 


—15 


59 


—82 


22 


22 


237 


186 


129 


51 


62 


14 


23 


398 


338 


—32 


—101 


—99 


—138 


24 


315 


222 


61 


15 


—16 


—22 


25 


349 


236 


17 


1 


—50 


—36 


26 


304 


238 


72 


—1 


—5 


—38 


27 


359 


233 


7 


4 


—60 


—33 


28 


352 


265 


14 


—28 


—53 


—65 


29 


373 


184 


—7 


53 


—74 


16 


30 


372 


232 


—6 


5 


—73 


—32 


31 


383 


303 


—17 


—66 


—84 


—103 


32 


345 


220 


31 


17 


—46 


—20 


33 


452 


239 


—86 


—2 


—153 


—39 


34 


502 


281 


—136 


—44 


—203 


—81 


35 


5S8 


603 


—222 


—366 


—289 


—403 


36 


289 


240 


77 


—3 


10 


—40 


37 


460 


326 


—94 


—89 


—161 


—126 



The Reliability of the Tests 



37 



In calculating the correlations for the Good group alone, the 
Poor group alone, and both groups together, the deviations of 
each individual were measured from the following as central 
tendencies : 



Memory of Passages 
Memory of Words . . 

A test 

Adding 

Learning Pairs 

Recognizing Forms . 
Ebbinghaus test .... 
Drawing Lengths. . . 
Estimating Lengths. 

Scroll 

Completing Words. . 

Easy Opposites 

Hard Opposites .... 
Geometrical Forms . 



Median of 
Good Group 



69 

29 

261 

200 

24 

21 

418 

35 

61 

72 

144 

127 

1014 

164 



Median of 
Poor Group 



23 

19 

366 

320 

4.5 

9 

209 

32 

58 

128 

332 

295 

2623 

237 



Median op 
Good and 

Poor 
Together 



43.5 

23 
299 
240 
9.25 

13 
289 

33.5 

59 

90 

167 

184 

1903 

200 



38 



Correlations of Mental Abilities 



The deviation of each individual from each of these medians 
in each test, is shown in tables V a, V b, and V c.^ 

In calculating coefficients of correlation corrected for attenua- 
tion, it is necessary to have two sets of deviations from the cen- 
tral tendency in each case, one set for the first trial and one for 
the second. These deviations are given in tables VI a, VI b, and 
VI c,'^ and are measured from the following as central ten- 
dencies : 





Median of 
Good Group 


Median of 
Poor Group 


Median of 

Combined 

Groups 




Test I Test II 


Test I Test II 


Test I Test II 


Memory of Passages 

Memory of Words 

A test 


31.5 33.5 
15 14 
122 142 
101 94 
8 12.5 

10 10 
65 60 

479 518 

188 227 

38 34 

88 83 

70 71 

11 14 
30 30 


12.5 11. 
9 9 
184 170 
15 170 
2.7 2.4 
4 3.5 
136 134 
1149 1463 
117 92 
63 61 
122 108 
176 157 
18.5 15.5 
28 28.5 


20 23.75 
11.2 11.8 
144 148 


Adding 


116 134 


Learning Pairs 

Recognizing Forms 

Easy Opposites 


4 5.8 

7.8 7.8 
88 86 


Hard Opposites 

Ebbinghaus test 

Scroll 

Geometrical Forms 

Completing Words 

Drawing Lengths 

Estimating Lengl hs 


844 1041 
158 138 
43 47 
110 94 
91 77 
15 14 
29 30 



^ A sample page only is printed here, the full table being on file in the 
Library of Teachers College, Columbia University. 



The Reliability of the Tests 



39 



TABLE Va 
Deviations from the Median — Good and Poor Subjects Combined 















^^ 




















0) 










DQ 










+i 










f 






m 




rr, =3 




00 






03 






a 




u •■ — 




e 




o 

0) 

o 


o 
o 

a 


3 
o 

a 


CQ 
O 


O 

o 
'u 
a; 

a 

o 


be 


o 
bO 

"Si 

a 


Ph 

bD 

g 


o 

fcC 

'S 

bjD 
O 
o 


o 
a, 
&i 
O 
>> 

02 


d 






-< 


O 


< 


O 


^ 




C3 


1 


30J 


14 


43 


36 


143 


75 


5f 


14 


102 


2 


34i 


11 


62 


96 


83 


45 


141 


6 


106 


3 


26 


15 


19 


38 


45 


46 


281 


11 


54 


4 


321 


13 


39 


—5 


37 


34 


131 


8 


74 


5 


33i 


5 


35 





40 


27 


27i 


12 


36 


6 


28i 


15 


41 


36 


15 


64 


9i 


10 


40 


7 


201 


2 


—15 


8 


—1 


—27 


— 2i 


7 


82 


8 


141 


2 


38 


6 


119 


23 


191 


8 


57 


9 


16i 


13 


—15 


22 


13 


57 


201 


9 


81 


10 


23i 


4 


79 


55 


54 


—46 


1 


5 


21 


11 


25+ 


3 


86 


37 


75 


9 


If 


12 


75 


12 


27| 


6 


19 


—24 


62 


12 


201 





33 


13 





4 


105 


68 


40 


20 


14i 


11 


65 


14 


3i 





31 


65 


1 


—30 


3| 


7 


38 


15 


—141 


6 


44 


48 


64 


36 


21i 


3 


79 


16 


6i 


8 


2 


22 


—53 


3 


15J 


11 


50 


17 


26 








18 


—22 


—69 


31 


3 


46 


18 


1 





74 


—3 


70 





— u 


—2 


—16 


19 


-5J 


—4 


45 


8 


+ 72 


—107 


— 2i 


—1 


9 


20 


81 


2 


—78 


—73 


—123 


—134 


— 6i 


—10 





21 


n 


—2 


—82 


22 


—278 


—227 


— 4i 


—4 


—43 


22 


—26 


—2 


62 


14 


—68 




1 


2 


—49 


23 


—J 


4 


—99 


—138 


—110 


—365 


— 3| 


—6 


—53 


24 


—3+ 


—3 


—16 


—22 





39 


— 5i 


— 3 


—37 


25 


— 20i 


—4 


—50 


—36 


30 


—157 


1 


—17 


—95 


26 


-81 


—5 


—58 


—38 


—106 


—174 


-4i 


—3 


—144 


27 


-211 


—8 


—60 


—33 


—47 




1 


—4 


—5 


28 


—22 


—3 


—53 


—65 


—67 


—28 


—n 


—4 


—19 


29 


-20^ 


—6 


—74 


16 


25 


—24 


— 3i 


1 


—128 


30 


—14 


—4 


—73 


—32 


—326 


—248 


—51 


—11 


—133 


31 


— 29.| 


—7 


—84 


—103 


—245 




—\ 


—1 


—205 


32 


— 22i 


—6 


—46 


—20 


—90 




-7i 


—9 


—128 


33 


—301 


—9 


—153 


—39 


—62 




— 8i 


—9 


—524 


34 


—191 


—9 


—203 


—81 


—306 


—623 


—n 


—1 


—136 


35 


—43+ 


—15 


—287 


—403 


—70 


—327 


— 6i 


—6 


—191 . 


36 


— 28| 


—5 


10 


—40 


—392 




-6i 


—3 


—337 


37 


—381 


—11 


—161 


—126 


—293 




-8i 


—10 


—653 



40 Correlations of Mental Abilities 

TABLE Vb 
Deviations from the Median of the Good Subjects Only 















^ 




— ' — 






^ 




























CO 






























5_, 
















o 


(^ 


O 




o 

fa 




o 




o 

fa 






CO 3 


15* 
CO 


o 






"3 


a 
.2 




PL, 

a 




O 
Oh 

o 


o 
ex 

o 




*4H 

o 


o 

a 


i 


0) 


o 


'-+3 

is 


a 




bO 
O 


>> 

«3 


V ■ 


a 
IS 


6 


<o 


OJ 


"^ 


a 


-c 


o 


0) 


''^ 


<S 


c3 


,i2 


fe 


s 


§ 


<!^ 


O 


< 


6 


>^ 


^ 


w 


w 


fa 


1 


4| 


8 


5 





103 


52 


—9 


6 


45 


397 


343 


2 


9 


5 


24 


60 


43 


22 





—2 


49 


233 


57 


3 


I: 


9 


—19 


2 


5 


23 


14 


3 


—3 


342 


260 


4 


n 


7 


1 


—41 


—3 


11 


—1 





17 


237 


—24 


5 


8i 


— 1 


—3 


—36 





4 


13 


4 


—21 


—4 


54 


6 


21 


9 


3 





—25 


41 


— 5i 


2 


—17 





—21 


7 


— 4| 


—4 


—53 


—28 


—41 


—50 


—17 


— 1 


25 


203 


20 


8 


— lOf 


—4 





—30 


79 





5 








—52 


3 


9 


— 9i 


7 


—53 


—14 


—27 


34 


6 


1 


24 


20 





10 


-2i 


—2 


41 


19 


14 


—69 


—14 


—3 


—36 


—179 


—54 


11 


—03 


48 


1 


35 


—14 


—13 


4 


18 


96 


106 


12 


If 





—19 


—60 


22 


—11 


6 


—8 


—24 


—283 


22 


13 


—25* 


—2 


67 


32 





—3 





3 


8 


—144 


—84 


14 


— 22i 


—6 


—7 


29 


—39 


—53 


—11 


—1 


—19 


—502 


—55 


15 


— 40-i- 





6 


12 


24 


13 


6* 


—5 


22 


177 


—67 


16 


—19 


2 


—36 


—14 


—93 


—20 


X 


3 


—7 


—529 


—10 


17 


h 


— 


—38 


—18 


—62 


—92 


—11 


—5 


—10 


—330 


—92 












TABLE 


Vc 












Deviations from the Median of the Poor Subjects Only 




18 


21i 


4 


141 


34 


150 


165 


3* 


2 


95 


692 


133 


19 


15 





112 


45 


152 


58 


21 


3 


120 


720 


80 


20 


29i 


6 


—11 


—36 


—43 


31 


—n 


—6 


111 


893 


68 


21 


28 


2 


—15 


59 


—198 


—62 


i- 





68 


182 


—8 


22 


—5-1 


2 


129 


51 


12 




5i 


6 


42 


267 


55 


23 


20 


8 


—32 


—101 


—30 


—200 


1 


2 


58 


325 


* 


24 


17 


1 


61 


15 


80 


204 


—h 


1 


74 


—441 


54 


25 








17 


1 


110 


8 


5h 


—13 


16 


389 


60 


26 


IH 


— 1 


72 


—1 


—26 


—9 


i^ 


1 


—33 


607 


50 


27 


-li- 


—4 


7 


4 


33 




H 





100 


645 


.1. 


28 


—1* 


1 


14 


—28 


13 


137 


—2h 





92 


501 


66 


29 


o' 


— 2 


—7 


53 


105 




H 


5 


—17 


—228 


+ 


30 


6i 





—6 


5 


—246 


—83 


—1 


—7 


—22 


—561 


—89 


31 


—9 


—3 


—17 


—66 


—65 




4-i 


3 


—94 


—617 


—32 


32 


— 1| 


—2 


31 


17 


—10 




—2^ 


—5 


—17 


—183 


—49 


33 


-lOi 


—5 


—86 


—2 


18 




— 3A 


— 5 


—413- 


-1417 


—208 


34 


1 


—5 


—136 


—44 


—226 


—458 


—2% 


3 


—25 


—804 


—86 


35 


—23 - 


-11 


—222 


—366 


10 


—162 


— U 


—2 


—80 


—664 


—74 


36 


—8 


— 1 


77 


—3 


—312 




— li 


1 


—226 


—751 


—80 


37 


-18i 


—7 


—94 


—89 


—213 




-3i 


—6 


—542 


—779 


—208 



The Reliability of the Tests 



41 



TABLE VI 

Deviations from the Median — First and Second Trials — All 
Subjects Combined 





I— 1 


t3 














tg 


T3 




oT 


oT 








■ 






rH 


(N 




<o 


a> 






-M 


Tj 












6X1 


bO 






CO 


a 






oT 


oT 




cS 


o3 






I— 1 


(M 






T) 


TS 




02 
















I-, 


t^ 


-8 


^ 

^ 


fS 






'3 


§ 

3 




■Td 





i 


15° 


«+-! 


=«-t 




TS 


Plh 


P-i 


■g 


PI 


C4H 


«*-! 



w. 





c 


to 
I— 1 




be 

el 


be 

.S 


i-i 


bc 



b 



b 











tf 


-+^' 


'3 


"S 


fl 


a 










a 


a 


<D 


O) 


o3 


^ 


-3 


''Q 


a 


a 


6 


as 


03 


'*"' 


"*"* 


0) 


03 


T3 


■73 


0) 


(U 


12; 


§ 


§ 


< 


< 


^ 


^ 


<! 


< 


s 


s 


1 


161 


13| 


23 


13 


1 


4.2 


62 


91 


6.8 


7.2 


2 


17i 


161 


44 


11 


8 


6.2 


31 


62 


8.8 


2.2 


3 


lOf 


15 


30 


—18 


15 


13.2 


26 


29 


6.8 


8.2 


4 


15| 


16| 


23 


9 


4 


9.2 


24 


23 


7.8 


5.2 


5 


m 


16t 


—22 


6 


13 


14.2 


7 


43 


3.8 


1.2 


6 


lOi 


174 


18 


16 


34 


5.2 


—15 


40 


6.8 


8.2 


7 


13 


74 


22 





1 


—3.8 


5 


4 


— .2 


2.2 


8 


64 


8 


26 


5 


7 


12.2 


58 


71 


— .2 


2.2 


9 


8 


8 





—22 


9 


11.2 





23 


5.8 


7.2 


10 


Hi 


114 


44 


28 





.2 


24 


40 


1.8 


2.2 


11 


m 


51 


46 


33 


1 


.2 


15 


70 


1.8 


1.2 


12 


15i 


114 


11 


1 


9 


11.2 


21 


51 


4.8 


1.2 


13 


H 


—14 


52 


46 


4 


10.2 


15 


35 


2.8 


1.2 


14 


14 


H 


18 


6 


2 


1.2 


11 





—1.2 


1.2 


15 


-H 


— -51 


12 


25 


84 


12.2 


24 


50 


— .2 


6.2 


16 


3i 


3 


5 


—10 


8 


6.7 


—30 


—13 


4.8 


3.2 


17 


114 


14i 


—4 


—3 


2 


1.2 


—10 


—2 


— .2 


.2 


18 


—2 


2i 


26 


31 





—1.8 


42 


38 


.8 


— .8 


19 





-54 


19 


19 


—1 


—1.8 


46 


36 


—3.2 


— .8 


20 


H 


5i 


—18 


—67 


—2 


—4.8 


—37 


—76 


1.8 


.2 


21 


41 


3 


—92 


3 


—1 


—3.8 


—146 


—122 


— .2 


—1.8 


22 


—12 


—144 


7 


48 


—1 


1.2 


—18 


—40 


— .2 


—1.8 


23 


—4 





—53 


—53 


-4 


—3.8 


—65 


—35 


3.8 


.2 


24 


-2| 


—1 


8 


—31 


—2. 


—3.8 


11 


— 1 


— .2 


—2.8 


25 


—9 


—114 


—45 


—12 





2 


9 


31 


— .2 


—3.8 


26 


—54 


-34 


—13 


1 


—14 


—3.3 


—59 


—37 


—3.2 


—1.8 


27 


—94 


-124 


—36 


—31 





2 


—15 


—22 


—2.2 


—5.8 


28 


—9 


-13i 


—33 


—27 


—3 


—4.8 


—51 


—6 


.8 


—3.8 


29 


—8 


—121 


—68 


—13 


—1 


—2.8 


11 


+ 24 


—2.2 


—3.8 


30 


—H 


—11 


—54 


—26 


—1 


—5.3 


—113 


—203 


—2.2 


—1.8 


31 


— 13i 


—164 


—71 


—20 





— .8 


—115 


—120 


—1.2 


—5.8 


32 


—7 


—154 


—28 


—25 


—4 


—3.8 


—42 


—38 


—3.2 


—2.8 


33 


—14 


—17 


—143 


—17 


— 3 


—5.8 


—21 


—31 


—4.2 


—4.8 


34 


-2i 


— 17| 


—126 


—84 


—3 


—4.8 


—157 


—139 


—2.2 


—6.8 


35 


—20 


— 23f 


—134 


—162 


—4 


—2.8 


—43 


—17 


-10.2 


—4.8 


36 


— 14f 


—14 


—1 


4 


—3 


—3.8 


—191 


—191 


—2.2 


—2.8 


37 


-161 


—221 


—28 


—40 


—4 


—4.8 


—110 


—173 


—3.2 


—7.8 



42 



Correlations of Mental Abilities 



TABLE VII 

Reliability of the Tests, as Shown by the Pearson Coefficients of 
Correlation Between First and Second Trials (Raw Coefficients) 

In the case of each test the heavy-face figure given first is for the Good 
and Poor together, divergences being measured from the median of the 37 
individuals. The second figure is for the Good group, divergences being 
measured from its median. The third figure is for the Poor group. 

92 



Ebbinghaus test 


First 4 trials and last 4 


96 
93 


Hard Opposites 


« 


2 " " " 2 


97 

60 

88 


Memory of Words 


11 


2 " " " 2 


73 

48 
49 


Easy Opposites 


11 


2 . « « « 2 


93 

53 

89 


A test 


it 


trial and second 


72 

62 
60 


Memory of Passages 


a 


2 trials and last 2 


90 

78 
83 


Adding 


u 


trial and second 


91 

76 
90 


Geometrical Forms 


u 


« (I a 


90 

69 
91 


Learning Pairs 


u 


2 trials and last 2 


93 

79 
52 


Recognizing Forms 


(1 


trial and second - 


40 

-41 
-10 


Scroll 


u 


76 

« « « _04 
71 


Completing Words 


u 


« » a 


92 

27 
89 


Drawing Lengths 


u 


4 trials and last 4 


72 
42 
95 


Estimating Lengths 


" 


trial and second ' 


48 

47 
60 



The Reliability of the Tests 43 

The reader should remember that correlations for Good, for 
Poor, and for Good and Poor together will have these meanings 
throughout. 

2. Detailed discussion of the reliability of each test 

The reliability of any test will be measured by the closeness 
of the correlation between the two different trials with it. Table 
VII gives these " coefficients of reliability " for the different 
tests. Just what the two trials were in each case can be found 
in the appendix on pages iii to 121. 

The reliability of the A test was satisfactory, though not as 
high as could be desired. The correlation between trials i and 2 
was about 66 (72 taking the Good and Poor together, 62 taking 
the Good group alone, and 60 taking the Poor group alone). 
It would have been well worth the extra labor to have taken 
four trials instead of only two, for the sake of the added relia- 
bility of the results. The arrangement of the letters is such as 
to make the test a good one of its kind. 

The Geometrical Forms test seems to be somewhat higher in 
reliability than the A test, the correlations between marking 
hexagons and marking semi-circles being 69 for the Good, 91 
for the Poor, and 90 for both taken together. This may be 
owing to the fact that some members of the Poor group were 
handicapped by lack of familiarity with geometrical forms, mak- 
ing those least familiar with such forms stand lowest in both 
trials. In so far as this is the case, it simply means that what is 
tested is a combination of factors involved in the A test plus 
familiarity zvith the geometrical forms. 

The Scroll test as given is of doubtful reliability. Taking the 
Good group by themselves the correlation between the first and 
second tests is practically zero. For the Poor group the correla- 
tion is 71, and for both together it is y6. To get reliable re- 
sults from it, at least two or three practice trials should be given 
first so that all could learn to do it at a fairly uniform speed. 
Unless the rate of performing the test is fairly uniform, it is 
probably impossible to find a method of scoring that is entirely 
satisfactory. It is curious that the coefficient of reliability 
should be so much higher in the Poor group than in the Good 
group (71 in the Poor and — 4 in the Good). While conclu- 



44 Correlations of Mental Abilities 

sions as to the cause of this are somewhat uncertain, the figures 
indicate that the test brought out individual differences in the 
Poor group, but not in the Good. What these differences are, 
is the doubtful point. They are probably in part due to dif- 
ferences in practice in handling pens and pencils. It is easy 
to see, however, that there would be a positive correlation in 
these days between intelligence and practice in handling pen and 
pencil, as few people would be in a position to make use of 
average intelligence without some occasion to use pen or pencil. 
It seems fairly probable that the high reliability in the Poor 
group is due also in part to the fact that some did poorly in 
both trials owing to poor muscular control, on account of lack 
of steadiness of hand. These two factors would operate to- 
gether, to make those who did best in the first trial do best in 
the second also. In the Good group, on the other hand, all had 
had plenty of practice in handling pen and pencil, and none 
showed decided lack of steadiness of hand, so that individual 
differences here were mainly in the mode of adaptation to this 
new test. Subjects in the Good group tended to vary their 
method in the two trials much more than the subjects of the 
Poor group, and two trials did not give time enough to allow 
the best method to become fixed in time to materially improve 
the subject's score. Had there been about ten trials taken, the 
advantages of rapid and skillful adaptation to this kind of thing 
would in all probability have had a chance to show themselves 
in the last few trials at least. If so, this would have resulted 
in increased reliability. The test could be shortened about one- 
third with advantage, as in some cases there was evidence of 
fatigue before a trial was completed. It is also somewhat ob- 
jectionable on account of tending to cause eye strain and dizzi- 
ness. 

The reliability of the next test. Easy Opposites, is satisfac- 
tory. The coefficients of correlation between trial i and trial 
2 are: Good 53, Poor 89, all together 93. It appears to be 
a good test of readiness of controlled associations. To persons 
of average ability the words in the lists are familiar from or- 
dinary conversation, and little effort is required to recall a satis- 
factory opposite for each. In so far as little hesitation is neces- 
sary to get any desired opposite, the test is a good measure of 



The Reliability of the Tests 45 

rapidity of association. In some cases, however, a word that 
is easy for many may cause considerable loss of time to one or 
two. In the case of a few of the Poor subjects, their facility in 
handling even these words was so slight that the test was for 
them very much like the Hard Opposites test for the more able 
subjects. For those making the poorest records in this test, get- 
ting the proper opposites seemed to call for an exercise of their 
best thinking capacity. They thought of the words in sentences, 
and then of the opposites, and then selected the best by elimina- 
tion of the more unsatisfactory ones, whereas to the best sub- 
jects the correct opposites were suggested with a minimum of 
effort and hesitation. For the Poor subjects this is then a test 
of selective thinking. 

Test V, Recognizing Forms, was not, as given, satisfactory 
in regard to reliability. The coefficients were: Good — 41, Poor 
— 10, all together 40. The variability of the two trials is so great 
as to swamp small differences, such as occur within either group, 
and to show only very crudely the larger differences between an 
individual in the Good, and one in the Poor group. 

Test VI, Memory of Words, was fairly satisfactory as to re- 
liability, the correlations between the average of the first two 
trials, and the average of the last two being : 62 for the Good, 
60 for the Poor, and 72 for all together. The reliability could of 
course be improved considerably by giving eight trials instead 
of four. The labor involved in doing this would be well repaid 
by the gain in reliability. As to the number of words to be 
given, sixteen was undoubtedly so many as to be somewhat dis- 
tracting to several of the Poor group. The number of words 
best adapted to the Good group would probably be too many 
for securing most accurate results from the members of the 
Poor group. On the whole, twelve words would seem to be the 
optimum number. Eleven out of sixteen was the highest score 
secured by anyone. 

Test VII, Learning Pairs, was satisfactory in reliability, the 
coefficients of correlation between the two halves of the test 
being: Good 79, Poor 52, and all together 93. It appears to be 
a good test for a certain type of ability to form and use asso- 
ciations. 

Test VIII, Mem.ory of Passages, showed a correlation be- 



46 Correlations of Mental Abilities 

tween the two halves of the test of 78 for the Good, 83 for the 
Poor, and 90 for all together. The four passages of one hun- 
dred words each were selected with a view to eliminating as far 
as possible specialized individual differences and interests. The 
passages were selected from newspapers, on the presumption 
that people in general are more nearly on an equality of interest 
in the case of that style of reading matter than in the case of 
any other matter that might be chosen. The more the indi- 
vidual was interested in the particular subject matter chosen, 
and the more he knew about it, the better he would be able to 
assimilate and remember it. It is therefore apparent that any 
test of this kind cannot fail to be, more or less, a test of breadth 
of interest, as well as a test of memory. In fact, range of in- 
terest would be one common factor in power to memorize pas- 
sages and in general intelligence. 

Test IX, Drawing Lines, proved fairly satisfactory as given. 
The correlations between the first four trials and the last four 
were: 42 for the Good, 95 for the Poor, and ^2 for all to- 
gether.^ It was evident to the experimenter that it was in part 
a test of pains taking and patience. In some cases subjects would 
be undecided as to whether to make any change in the length 
of the line they had drawn, and then on deciding to change it, 
would do so to the extent of 4 to 6 mm. It was evident that 
most subjects did not manage to discriminate length as closely 
in this test as in the test in comparing lengths shown in pairs. 
It would have been rather better to have taken four trials of 
each length instead of only three. 

Test X, Estimating Lengths, was hardly satisfactory in re- 
liability as given. The coefficients of correlation for the first 
half of the test and the second half were: 47 for the Good, 60 
for the Poor, and 48 for all combined. Half of the test as 
given was too easy to bring out individual differences. It would 
have been better to have made the differences 1, 2, 3, and 4 mm. 
respectively, instead of 2, 4, 6, and 8 mm. respectively. While 
this method would enable one to get more accurate results as 



^ For purposes of comparison, the experimenter also took the trouble to 
calculate the coefficients of reliability in a slightly different way in this 
test. The average of the correlations of the ist trial with the 2nd, 2nd 
with 3rd, and ist with 3rd, gives 68 for the Good group, 86 for the Poor, 
and 82 for the combined groups. 



The Reliability of the Tests 47 

to ability to compare lengths of lines than test IX, it must be 
carried out far more extensively than that test, if reliable 
scores on a sufficiently fine scale are to be secured. The diffi- 
culty here, of course, is due to the fact that the use of the 
method of right and wrong cases makes the test a long one, as 
so many trials have to be given. It would doubtless be worth 
the trouble to find out by experiment to what extent scores on a 
basis of relative position from a comparatively short series of 
tests such as those described here, would differ from scores se- 
cured from a long and elaborate series of tests sufficiently ex- 
tensive to justify the exclusive use of the method of right and 
wrong cases in scoring. 

The coefficients in the Adding test were : 76 for the Good 
group, 90 for the Poor, and 91 for all together. The fact that 
the coefficient is slightly higher for the Poor group than for 
the Good is probably to be explained by two reasons. First, 
there was m.ore variation in amount of practice in adding in the 
Poor group; second, in general in all tests correlated with intel- 
lect there was more variability in the scores of the Poor group 
than in those of the Good group. In other words, the Goods 
were a more homogeneous group in respect to addition than the 
Poors. 

In the Hard Opposites test, the coefficients of correlation be- 
tween the two halves of the test were : 60 for the Good, 88 for 
the Poor, and 97 for all together. As in the Adding test, the 
reliability was considerably higher for the Poor group than for 
the Good. It is a good test, though it could no doubt be im- 
proved somewhat by leaving out some of the most difficult 
words, and by carefully selecting lists of words more nearly 
equal to one another in difficulty. This would be by no means 
easy to do, as words which are familiar to many may chance 
to be little used by a few. However, a word whose opposite is 
so difficult for most people as the word unless had better be 
omitted, as a large number omitted it altogether, while others 
spent much time in thinking out its opposite; and this makes it 
very difficult to score the results in a way that is just to both. 
Different tests of varying degrees of difficulty would be well 
worth devising and perfecting. With the least efficient members 



48 Correlations of Mental Abilities 

of the Poor group the test became one of range of vocabulary 
rather than of abihty to think up different opposites. 

Text XIII, Completing Words, or ta test, was not satisfactory 
in the case of the Good group. The coefficients of correlation 
between the two halves of the test were: 27 for the Good, 89 
for the Poor, and 92 for all together. On account of the greater 
variability of the Poor group, a less perfect test serves to bring 
out their comparatively marked individual differences, whereas 
on the other hand in a group that is more highly selected, and 
whose individual differences are not so pronounced, they may 
be easily obscured or covered up by " chance variation " due 
to imperfections in the test itself. Thus a member of the Good 
group might have a relatively high difference between his score 
in the first and second trials, owing to hesitation over the com- 
pletion of one or two words, while in the Poor group, the same 
amount of hesitation would not have nearly so much influence, 
as some of the slowest hesitated at practically all of the words, 
and only 5% of the Poor group reached the median of the Good 
group. 

From this it appears that the test as it is, is a fairly good 
one for bringing out group differences, but not perfect enough 
to bring out fine individual differences. It could be easily im- 
proved so as to make it satisfactory for this purpose as well. It 
would be better to have the syllables arranged in chance order 
instead of as they were, so as to avoid such very easy sequences 
as ha-t, ca-t, da-te, ea-t, fa-t, ga-te, etc. The test could also 
be improved by eliminating some of the most difficult of the 
syllables. Two or three tests carefully graded in difficulty 
vs^ould be well worth trying out, but it seems to the writer that 
the most significant and reliable results would be obtained from 
the use of combinations that could be completed quickly and 
with little hesitation over single words. 

Test XIV, Ebbinghaus mutilated test, was very high in relia- 
bility as used, easily the highest of all. The coefficients or cor- 
relation between the two halves of the test are: 96 for the 
Good, 93 for the Poor, and 92 for all together. It is beyond 
question a good test, and should be perfected and standardized, 
with a considerable number of specimens graded in difficulty. 

Test XV, Absurdities, was discarded, as far as calculating 



The Reliability of the Tests 49 

correlations with other tests was concerned, on account of im- 
perfections in the test itself, which made it difficult to find a 
satisfactory method of scoring the results. In general, sheet A, 
(see appendix, page 121), seems rather too easy to be of much 
value. 
No. I was missed by only i good subject, and by 5 of the poor 

group. 
No. 2 was wrongly marked by i good subject, and by 5 of the 

poor group. 
No. 3 was wrongly marked by i good subject, and by 6 of the 

poor group. 
No. 4 was omitted by i good subject, and by 3 of the poor 

group. 
No. 5 was omitted by 4 good subjects, and by 5 of the poor 

group. 
No. 6 was wrongly marked by o good subjects, and by 3 of the 

poor group. 
No. 7 was omitted by o good subjects, and by o of the poor 

group. 
No. 8 was wrongly marked by o good subjects, and by 3 of the 

poor group. 
No. 5 is of doubtful absurdity, and should be thrown out, 
while No. 7 should be thrown out on account of being too 
evident. 

In sheet B (see appendix, page 121), 
No. I was wrongly marked by 6 good subjects and by 3 of the 

poor group. 
No. 2 was omitted by i good subject, and by 8 of the poor 

group. 
No. 3 was omitted by o good subjects, and by 6 of the poor 

group. 
No. 4 was wrongly marked by o good subjects, and by 2 of the 

poor group. 
No. 5 was omitted by i good subject, and by 4 of the poor 

group. 
No. 6 was wrongly marked by i good subject, and by 3 of the 

poor group. 



50 Correlations of Menial Abilities 

No, 7 was wrongly marked by i good subject, and by 4 of the 

poor group. 
No. 8 was omitted by 8 good subjects, and by 8 of the poor 

group. 
No. I should be thrown out on account of general uncertainty 
as to its absurdity, and No. 8 on account of the ambiguity of 
the word " dummy." 

In sheet C (see appendix page 122), 
No. I was wrongly marked by i of the good group, and by 3 of 

the poor. 
No. 2 was omitted by 4 of the good group, and by 9 of the 

poor. 
No. 3 was omitted by 6 of the good group, and by 10 of the 

poor. 
No. 4 was wrongly marked by o of the good group, and by 6 of 

the poor. 
No. 5 was omitted by 4 of the good group, and by 14 of the 

poor. 
No. 6 was omitted by i of the good group, and by 8 of the 

poor. 
No. 7 was wrongly marked by 2 of the good group, and by 4 of 

the poor. 
No. 8 was wrongly marked by 15 of the good group, and by 7 

of the poor. 
No. 3, while missed by 6 of the Good group, can hardly be 
considered a poor test unless it be that the wording is somewhat 
faulty, for practically everyone knows that the cream rises to 
the top. In most cases the failures here were due simply to 
not applying the familiar information, and so failing to make 
the simple deduction. Some, however, found fault with the 
wording, and would not admit the absurdity when pointed out. 
If worded, "As everyone knows, a pint of cream weighs slightly 
more than a pint of milk," this objection would be overcome. 

No. 5 is sufficiently doubtful to be excluded. This is further 
substantiated by the fact that of 20 advanced students and pro- 
fessors who afterwards marked the sentences at their leisure, 
only 9 marked it as absurd, and i as doubtful. No. 6 would of 
course be faulty if the name Pontius Pilate were unfamiliar to 



The Reliability of the Tests 5 1 

any of those tested. Perhaps John the Baptist, or Julius Caesar 
would be preferable. No. 8 should be thrown out on account 
of ambiguity. 

In sheet D, (see appendix page 122), 
No. I was wrongly marked by o of the good group, and by 6 of 
, the poor. 

No. 2 was omitted by 5 of the good group, and by 8 of the 

poor. 
No. 3 was omitted by 4 of the good group, and by 13 of the 

poor. 
No. 4 was wrongly marked by 8 of the good group, and by 8 of 

the poor. 
No. 5 was wrongly marked by o of the good group, and by 3 of 

the poor. 
No. 6 was omitted by 2 of the good group, and by 9 of the 

poor. 
No. 7 was omitted by 4 of the good group, and by 9 of the 

poor. 
No. 8 was wrongly marked by 7 of the good group, and by 12 of 

the poor. 
Some who missed No. 3 would not afterwards admit its ab- 
surdity on the ground that there is nothing absurd about the 
statement that some states have very absurd laws. While this 
objection does not seem to the writer to be very well taken, it 
would be better to find a re-wording of the point which would 
not be open to this objection. No. 7 should be thrown out as its 
absurdity is open to question. No. 8 however is not absurd, in 
spite of its being marked as such by 4 of the good group, and 
marked as doubtful by 3 others. It was not marked as absurd 
by any of the advanced students and professors who marked 
the absurdities at leisure. 

If the records are scored by the plan originally intended, in 
spite of the imperfections pointed out above, the group dif- 
ferences brought out by the test would be considerable. None 
of the Poor group reach the median of the Good group, 25% 
of the Poor group reach the lowest 4 of the Good group, and 
70% of the Poor reach the lowest i of the Good group. Of 
course this simple scoring does not take into account the time 



52 



Correlations of Mental Abilities 



element at all, and as the test zvas given, no scoring would be 
fair which did not take the time element into account. While 
the same instructions were given to all, the members of the 
Poor group took their leisure to a far greater extent than mem- 
bers of the Good group. There is no doubt that many of the 
Good subjects would have made fewer mistakes if they had 
taken as much time as members of the Poor group. It seems 
to the writer that the best way to give the test would be to allow 
each subject the same amount of time for marking each sen- 
tence. 

While the results could be scored by throwing out the objec- 
tionable sentences and taking into account the time element, it 
seems hardly worth while to do so without improving and ex- 
tending the test. Its reliability as given would probably be low. 

An improved test of this sort would surely reveal character- 
istic individual differences, and with a sufficiently large number 
of sentences the reliability of the test could be made satisfac- 
tory as long as it had not been previously seen by the subject. 
Just how significant this ability is in relation to general intelli- 
gence, is of course doubtful, but the correlation would probably 
be fairly high. Undoubtedly the most and the worst mistakes 
were made by the most stupid of the Poor group. 



TABLE VIII 
Extent to Which the Poor Group Overlaps the Good Group 











^ 


















q 

c 


a 
rra 




Percentage of Poor 




o 


o 


1 


<o 




'T3 







a 


a 

c 




1-1 c 







Group Surpassing 


3 
d 


o 


O 


"o 


o 
a 




^ 


Ph 




03 


^c 




CO 


Co 


►-5 




J3 
C 

IS 


O 


o 


>> 

o 

a 

(a 


O 


c 
■S 


"S 

a 


.S 
'S 


1 


a 

c 


'c 
tc 

c 

0) 


■q 




a 


to 
a 

c5 




w 


W 


^ 


;y 


w 


< 


o 


I-! 


< 


O 


pi 





H 


w 


Q 


50% of good group .... 

















10 


5 





15 








15 


30 


55 


Lowest 4 " " " 234% 








5 


10 





20 


10 





20 


20 





10 


80 


40 


65 


" 2 " " " 12%. 


.5 





10 


1.5 





2.5 


15 





25 


25 





30 


PO 


55 


75 


" 1 " " " 6%. 


5 





10 


40 





30 


15 


30 


25 


35 


10 


35 


90 


00 


85 



Significance of Tests and Analysis of General Intelligence 53 

VI. Significance of the Tests and Analysis of General 
Intelligence as Shown by the Differences Be- 
tween THE Good Group and the Poor Group. 

I. Extent of overlapping in the different tests 

Table VIII summarizes the group differences brought out by 
the tests. 

The Ebbinghaus and the Hard Opposites tests separate the 
two groups almost completely. The only exception is the case 
of one of the Poor group who surpassed two of the Good group 
in the Ebbinghaus test. The subject in question is the only one 
of the Poor group who held a responsible position at the time, 
viz., that of Assistant Superintendent of the Salvation Army 
Industrial Home. This shows very decidedly the fact that in 
the powers called into play in these two tests, the Good group is 
far superior to the Poor. 

The Memory tests separate the groups decidedly, but not so 
completely as the two tests just mentioned. None of the Poor 
group reached the median of the Good group in either Memory 
of Words or Memory of Passages. Only 10 per cent of the 
Poors reached the lowest 12 per cent of the Goods in Memory 
of Words, and only 15 per cent reached this standard in Memory 
of Passages. As one of the Good group did very poorly in 
Memory of Passages, 40 per cent of the Poor group surpassed 
his record. It is possible that reading the memory tests instead 
of allowing the subjects to read them, i.e., making the tests audi- 
tory rather than visual, may in some cases have put members of 
the Good group at a disadvantage. 

The Learning Pairs test separates the groups completely, ex- 
cept that 30 per cent of the Poor group surpass the record made 
by the lowest one of the Good group. This test is, without 
doubt, somewhat more novel to the Poor group than to the 
Good, on account of the fact that the Good group have studied 
languages and vocabularies. 

The Recognizing Forms test also separated the two groups 
completely, except that 10 per cent of the Poor group reached 
the lowest one of the Good group. It is to be remembered, how- 
ever, that this test was not satisfactory from the standpoint of 
reliability. 



54 Correlations of Mental Abilities 

The Association test, Easy Opposites, and Adding, do not 
separate the two groups equally well. The Easy Opposites test 
does so completely, while in the Adding test lo per cent of the 
Poors reach the median ability of the Goods, 20 per cent of the 
Poors reach the lowest 24 per cent of the Goods, and 30 per 
cent of the Poors reach the lowest individual of the Goods. 

The fact that the estimated true correlation between Adding 
and Eas}^ Opposites is only 56 (see Table XIV), suggests that 
it is hardly justifiable to class them both under the same name 
— Association — if this is to imply that they are tests of the 
same thing. The low correlation is suggestive of disturbing fac- 
tors — probably different amounts of practice in Addition by the 
different subjects. At any rate the one is a language test and 
the other is not. The Easy Opposites test also seems to re- 
quire selective thinking, responding to the elements of a situa- 
tion and thinking things together, in the case of the Poor group, 
to an extent that the Addition does not. 

The Completing Words or ba- test stands about midway be- 
tween the Easy Opposites test and the Addition test in respect 
to the way in which it separates the two groups. There are 
5 per cent of the Poor group who reach the median ability of 
the Good group, 10 per cent who reach the lowest 24 per cent 
of the Goods, 15 per cent who reach the lowest 12 per cent of 
the Goods, and 15 per cent who reach the lowest one of the 
Good group. 

The Perception tests, A test and Geometrical Forms, separate 
the two groups to about the same extent. In the A test 15 per 
cent of the Poors reach the m.edian ability of the Goods, 20 
per cent of the Poors reach the lowest 24 per cent of the Goods 
in both tests, 25 per cent of the Poors reach the lowest 12 per 
cent of the Goods in both tests, while 35 per cent of the Poors 
reach the lowest one of the Goods in the Geometrical Forms 
test. 

The Scroll test will be seen by the table to divide the two 
groups to about the same degree as the Geometrical Forms test, 
though conclusions here are not to he much relied upon on ac- 
count of the low reliability of the test in the Good group. 



Significance of Tests and Analysis of General Intelligence 55 

The tests in Estimating Lengths and in Drawing Lengths 
show little difference between the two groups. In fact 55 per 
cent of the Poor group actually surpass the median ability of the 
Good group in Drawing Lengths, and 85 per cent of them are 
above the lowest one of the Good group. In Estimating Lengths 
the Good subjects are only slightly superior. 

Thus the tests reveal very marked differences in the two 
groups in language tests demanding selective thinking; marked 
but less difference in certain tests of memory; very decided dif- 
ferences in language tests demanding speed and accuracy in easy 
association; less difference in the more directly practiced and 
mechanical associations demanded in adding; in perception tests 
and in motor control the differences are somewhat less still ; and 
in discrimination of lengths they are least of all. 

That the differences brought out by the tests are not due merely 
to differences in training and education is demonstrable from 
facts which will be discussed in detail later. We believe it can 
be shown that by far the largest factor in causing these dif- 
ferences is the native capacity of the individual in question. 

2. Mental relationships revealed by Pearson coefficients of cor- 
relation 

The raw Pearson coefficients of correlation are given in Table 
IX. The top line gives the coefficient of correlation when all 
subjects are taken together, in one group of 37 persons. The 
second line gives the correlations secured when m.embers of 
the Good group are taken separately, and the last line, the cor- 
relations when the Poor subjects are taken by themselves. 

It will be noted that on the whole the correlations are con- 
siderably higher in the top lines, i.e., where the two groups 
are taken together. Again the correlations of the second line, 
i.e., correlations of the Good group by itself, will be seen to 
be somewhat lower on the average than those of the third line 
where the Poor group is taken separately. The only clear ex- 
ceptions to this are in the Adding test, and in the unreliable tests. 
In case of the Adding test, it is doubtless due to practice enter- 
ing as a disturbing factor. These differences in the amount of 



56 



Correlations of Mental Abilities 



TABLE IX 

Pearson Coefficients of Correlation, Raw 
In the case of each test the heavy-face figure given first is for the Good 
and Poor together, divergences being measured from the median of the '67 
individuals. The second figure is for the Good group, divergences being 
measured from its median. The third figure is for the Poor group. 































^ 


^ 






























ts 


tH 






























o 


o 






























i-t 


M 














<u 




m 




m 










4) 






o 


m 
T3 

O 

i 


d 




ho 
Oh 




B 

1 

"a 
o 


'3 


s 




•a 
a 

M 


hD 


|1 

h-1 


hO 3 




J3 

ho 


o, 
O 


>> 


a 
o 




>> 


he 


t-, 




'3 




» 


d 


to 

c 


hO 

S 




a 
'2 


73 


O 


03 


1 


o 

e 


'3 

T3 


a 

O 


'S 

n 


o 


1 


"S. 

i 


e 


■? 

rf 


t>3 




W 


w 


S 


K 


< 


s 


<: 


O 


hJ 


tf 


CO 


o 


K 


Q 


o 






98 


94 


79 


62 


91 


71 


54 


78 


88 


55 


42 


33 


25 




Ebbinghaus test 




58 

85 


54 
66 


42 
87 


-16 
65 


31 
56 


61 
65 


-05 
34 


09 
65 


54 
31 


15 
14 


47 
44 


23 
12 


01 
34 


-16 




00 




98 




84 


80 


64 


81 


79 


70 


73 


74 


52 


43 


26 


25 




Hard Opposites 


58 




53 


70 


12 


34 


67 


07 


16 


19 


32 


62 


-02 


06 


-18 




85 




63 


75 


49 


58 


48 


31 


49 


12 


-07 


34 


00 


16 


-03 




94 


84 




62 


55 


82 


49 


56 


73 


71 


53 


40 


28 


21 




Memory of Words 


54 


53 




36 


-10 


23 


21 


00 


32 


37 


-17 


07 


19-01 


-28 




66 


63 




59 


60 


73 


22 


52 


23 


15 


19 


29 


04 


05 


-08 




79 


80 


62 




57 


52 


68 


53 


42 


58 


45 


29 


38 


48 




Easy Opposites 


42 

87 


70 
75 


36 
59 




01-05 
36 56 


45 
46 


26 
28 


-09 
45 


26 
32 


00 
-02 


45 
13 


-05 
26 


-05 
47 


-17 




14 




62 


64 


55 


57 




55 


54 


73 


39 


51 


39 


59 


25 


22 




A test 


-16 
65 


32 
49 


-10 
60 


01 
36 




-03 
44 


57 
31 


54 

72 


-11 
49 


02 
07 


13 
-02 


11 
62 


-18-01 
17 03 


-17 




-30 




91 


81 


82 


52 


55 




53 


67 


59 


66 


54 


31 


28 


19 




Memory of Passages ...... 


31 


34 


23 


-05 


-03 




20 


-17 


01 


14 


16 


19 


-23 


-19 


-29 




56 


68 


73 


56 


44 




10 


37 


19 


06 


10 


13 


32 


03 


04 




71 


79 


49 


68 


54 


53 




45 


39 


47 


51 


57 


17 


25 




Adding 


61 
65 


67 

48 


21 

22 


45 
46 


57 
31 


20 
10 




16 
16 


14 
41 


15 
15 


61 
04 


63 
51 


-05 
-29 


-39 

22 


-47 




00 




54 


70 


56 


53 


73 


57 


45 




35 


49 


54 


56 


25 


25 




Geometrical Forms 


-05 


07 


00 


26 


64 


-17 


16 




-18 


13 


-19 


07 


-14 


33 


22 




34 


31 


52 


28 


72 


37 


16 




23 


18 


-06 


39 


01 


15 


-03 




78 


73 


73 


42 


39 


C9 


39 


35 




69 


36 


29 


26 


09 




Learning Pairs 


-09 
55 


16 
49 


32 
23 


09 
45 


-11 
49 


01 
19 


14 
41 


"o§ 




05 
21 


34 

-28 


55 
18 


31 
03 


-12 
23 


-07 




00 




88 


74 


71 


56 


51 


66 


47 


49 


69 




44 


37 


34 


28 




Recognizing Forms 


54 


19 


37 


26 


02 


14 


15 


13 


05 




-27 


48 


19 


49 


19 




31 


12 


15 


32 


07 


06 


15 


18 


21 




07 


-03 


26 


24 


09 




55 


52 


53 


45 


39 


54 


51 


34 


S3 


44 




31 


19 


27 




Scroll 


15 


32 


-17 


00 


13 


15 


61 


-19 


.^4 


-27 




10 


25 


-24 


-19 




14-07 


-19 


02 


-02 


10 


04 


-06 


-28 


57 




08 


-27 


11 


03 




42 


43 


40 


29 


59 


31 


57 


56 


29 


37 


31 




21 


07 




Completing Words 


49 


62 


07 


45 


11 


19 


63 


07 


55 


48 


10 




18 


-03 


-OS 




44 


34 


29 


13 


02 


13 


51 


39 


18-03 


08 




-09 


03 


-09 




33 


26 


28 


38 


25 


28 


17 


25 


26 


34 


19 


21 




24 




Estimating Lengths 


23 


-02 


19 


-05 


-18 


-23 


-05 


-14 


31 


19 


25 


IS 




09 


06 




12 


00 


04 


26 


17 


32 


-29 


01 


03 


26 


-27 


-09 




22 


24 




25 


25 


21 


48 


22 


19 


25 


25 


09 


28 


27 


07 


24 






Drawing Lengths (total er- 


01 


06 


-01 


-05 


-01 


-19 


-39 


33 


-12 


49 


-24 


-03 


09 




73 


ror) 


34 


16 


05 


47 


03 


02 


22 


15 


23 


24 


11 


03 


22 




78 


Drawing Lengths (variable 


-16 


-18 


-28 


-17 


-17 


-29 


-47 


22 


-07 


19 


-10 


-OS 


06 


73 




error) 


00 


-03-08 


14 


-30 


04 


00 


-03 


00 


09 


03 


-09 


24 


78 





Significance of Tests and Analysis of General Intelligence 57 

the correlation are of course due to the facts (i) that the 
groups represent different selections, and (2) that the points 
from which the deviations are measured are different. Thus 
(i) the correlation between height and weight would be greater 
if one took human beings of all ages than if one took only nine- 
teen-year-olds or only the new-born. Thus (2) the correlation 
between height and weight in the new-born would be greater if 
each baby's height and weight were treated as deviations from 
the average for all human beings of all ages, than it would be 
if each baby's height and weight were treated as deviations 
from the average of the new-born. Hence in our amalgamated 
group, as two extreme grades of ability are represented, and 
measured by the deviations from the approximate central ten- 
dency of all men, the correlations are high wherever the traits 
concerned are themselves correlated with general intelligence. 

Having in m.ind these facts that the size of the coefficient of 
correlation is affected by how the group chosen is selected, and 
by what central tendency is taken from which to measure the 
deviations to be related, the question arises, " What would be 
the true correlations if instead of taking two small selected 
groups, we took a very large group representing a normal dis- 
tribution of human minds ? " This question can be discussed 
only after we have first compared the raw correlations in this 
table with the probable true coefficients which would have been 
got, if the original measures had each been a perfect measure 
of the average conditions of the trait in question, in the indi- 
vidual in question, instead of a measure secured by only a few 
minutes' sampling of his ability. These probable true coeffi- 
cients obtained by the formula, 

Rpq= 4 are given in Table X. 

^7 Rp,p, -f- Rq,q, 

The coefficients of correlation to be used in correcting for 
attenuation the Pearson coefficients of correlation given in Table 
IX, are given in Tables XI, XII, and XIII. 

The deviation measures from which they are computed are 
given in Tables V a, V b, V c, VI a, VI b, and VI c. 



58 



Correlations of Mental Abilities 



TABLE X 

Pearson Coefficients op Correlation (Corrected for Attenuatioiv) 
In the case of each test the heavy-face figure given first is for the Good 
and Poor together, divergences being measured from the median of the 37 
individuals. The second figure is for the Good group, divergences being 
measured from its median. The third figure is for the Poor group. 





0) 


CD 

"m 
O 


IB 

o 

t 

o 


03 

"3 
o 
& 




CD 

CO 
CD 

a 




CD 

a 

O 


2 


CO 

1 

c 


w 

-a 

bD 

a 


CD 

bO 

c 

bO 

a 






O 


b 


o 




^ 


W) 




^ 


3 


bo 

a 


■■i 




G 
Xi 


T3 


o 

a 

0) 


CO 


+3 

c« 

C.) 


o 

a 


G 
'73 


a 

o 


o 


a 

o 




a 

'-+3 
m 




W 


W 


s 


w 


<) 


s 


< 


U 


>^ 


o 


Q 


w 






92 


92 


75 


68 


91 


71 


54 


72 


50 


26 


52 


Ebbinghaus test 




66 


67 


48 


03 


42 


55 


00 


22 


67 


-17 


28 






90 


78 


90 


76 


61 


63 


36 


73 


71 


27 


01 




92 




92 


81 


76 


86 


74 


64 


72 


70 


25 


55 


Hard Opposites 


66 




75 


93 


15 


45 


79 


07 


14 


100 


10 


-08 




90 




77 


78 


65 


64 


51 


33 


66 


49 


13 


-02 




92 


92 




68 


70 


89 


56 


67 


82 


51 


06 


59 


Memory of Words .... 


67 


75 




52 


-13 


41 


20 


06 


53 


100 


-23 


44 




78 


77 




70 


88 


100 


23 


56 


44 


43 -09 


16 




75 


81 


68 




71 


59 


70 


54 


43 


50 


53 


56 


Easy Opposites 


48 


93 


52 




05 


05 


45 


38 


-04 


100 


00 


-02 




GO 


78 


70 




51 


58 


50 


34 


64 


49 


43 


16 




68 


76 


70 


71 




60 


67 


94 


44 


84 


27 


57 


A test 


03 
76 


15 

65 


-13 

88 


05 
51 




14 

48 


59 
39 


68 
91 


-16 

72 


04 
88 


-10 
08 


-11 




13 




91 


86 


89 


69 


60 




66 


60 


63 


38 


12 


58 


Memorj^ of Passages . . 


42 


45 


41 


05 


14 




20 


-30 


-26 


35 


-24 


-36 




61 


64 


100 


58 


48 




15 


41 


22 


13 


09 


35 




71 


74 


66 


70 


67 


66 




44 


46 


77 


27 


17 


Adding 


55 


79 


20 


45 


59 


20 




13 


12 


86 


-49 


04 




63 


51 


23 


50 


39 


15 




19 


51 


70 


05 


-40 




54 


64 


67 


64 


94 


60 


44 




40 


61 


30 


35 


Geometrical Forms. . . 


00 


07 


06 


38 


68 


-30 


13 




-23 


00 


40 


-14 




36 


33 


56 


34 


91 


41 


19 




39 


32 


14 


07 




72 


72 


82 


43 


44 


63 


46 


40 




34 


04 


54 


Learning Pairs 


22 


14 


53 


-04 


-16 


-26 


12 


-23 




74 


-38 


61 




73 


66 


44 


64 


72 


22 


51 


39 




34 


20 


36 




50 


70 


51 


50 


84 


38 


77 


61 


34 




17 


22 


Completing Words. . . . 


67 


100 


100 


100 


04 


35 


86 


00 


74 




-04 


06 




71 


49 


43 


49 


88 


13 


70 


32 


34 




00 


-28 




26 


25 


06 


53 


27 


12 


27 


30 


04 


17 




56 


Drawing Lengths 


-17 


10 


-23 


00 


-10 


-24 


-49 


40 


-38 


-04 




-41 




27 


13 


-09 


43 


08 


09 


05 


14 


20 


00 




34 




52 


55 


59 


56 


57 


58 


17 


35 


54 


22 


55 




Estimating Lengths. . . 


28 


-08 


44 


-02 


-11 


-36 


04 


-14 


61 


06 


-41 






01 


-02 


16 


16 


13 


35 


-40 


07 


36 


-28 


34 





Significance of Tests and Analysis of General Intelligence 59 



pq 



&4 
ft, 

o 
o 

g 

03 S 
^ IS 

^ i 

M 

to 
O u 



to 



lO 



2 I 

o 
O 



'TS 






2 'eq:j3na'3 Sm^Buipsa 

\ 'eqiSuai SnT:jT3raps3 

2 'sq^Suaq; gnm-BJo; 

X 'sq^Suan[ SntM.BjQ 

Z 'spjo^ SnpaidraoQ 

X 'epjOj^ gnpa^dnioQ 

Z 'sire J Sainj'BaT; 

X 'sare<j Sntni'Ba'j 

Z 'snuo^j i'B0u:^8xii08£) 

X 'snuoji iBDU^ainoaQ 

Z '3atppv 

X 'Sntppv 

Z 'S9gBSSB J JO j?IOin8J^ 

X 'saSBSSBj; jo jCJ0Tn8i\[ 

z "\^^'^ V 

X •%SB% V 
2 'sa^jtsoddo J^s-eg 
X 's^:^^soddo As-eg 
g 'epiOjVi. JO j^Joraajif 
X 'spjOj^ii^ JO AjoTn8i\[ 
Z 'sa^isoddQ PJ'BH 
X 'sa^TSoddQ P-ibj-j 
Z '%S9\ snBqgmqqg; 
X '%S9'\ sti'BqSmqqa 



O T-l t^ 00 10 00 1-H 00 i-l Tf 03 CO O 00 (M to CO 00 10 00 "-H 03 00 
<>)C0C0C0r-(CCC0(MC<5i-llMC0OO'-l'-HC0C0'-lOC0M -"il 



m 05 i-H t> t^ 1-1 03 (M 00 1-1 •* i> CD CO o> i> 00 05 in i> (N^hoo 

<M'-l!NIMCp<NCO-*<N'-l>-l'-lr-i(NrHMOON'-l l^CCN 



.-lO«OC0lO00c0'-<00'-l<r5J>(NC0t^-<*<c0 OSCOOSi-hoOiO 

(at>50t>co50TifTtc5iicoioiO'*iocccoo3 coco I coco 

N (N ■* O 03 1^ O to '-I CO 03 1-1 (N CO O CO CO O ff<l 00 "-I CO 00 
CO I> CD l> O CO TfH CO ■* iM lO to CO ■* •* CO O3C0IM I COCO 



003iOrH t^CD(NOO3C0(NO00CVI 00t^t^'*0300NCO 
CO Tj, to CD lO in >0 lO CO 00 lO CD CO Tt< 03 ■* CO U5 10 1-1 IM rH (N 



t> CO t^ lO 1-H CO CO CO to lO i-f CO 1-t 00 (M (M IM lO 00 to 03 03 lO 

CO ir: CO to CO lO CO CD CO •* lO •* 03 co •* co •* t^ l> i-i "-i 1-< 



00 1-1 o ■^ ■* ^- to lO (N o o to Tj< o3 1> 1-1 00 r~ 1-1 00 03 1-1 in 

1> CD 00 1- m CD I> I> l> to l> CO to to C0 1* rtH> 00 (M (N CO ■* 



OOOi-l-^NO COCOCO-^OCOinW'-lOMOiOOCDi-l-* 

t>coooi>ict> 03i>'^;ot»cocomio-*-*cDcoco'^coin 



C^ t^ O CD 1-1 rH o CO 00 CO l> lO in ■* T)H CO o 05 1-1 1^ t^ o 
O300 C3 1> 00 00 00 00 in l> GO CD l> CO CO CD CO 00 00 IM th CO CO 

N ■* in U3 O O 1-1 in I> lO CO lO 03 03 N O 00 (M C3 1-1 1-H t- 
03 00 00 1- 00 CD lO CD CO 00 00 in CD ■<*< CO t> t- CO C0 1-1 1-1 CO CO 

<NOlC000000t^00CDinoi^rt<O'-iC<!i-l00COCDt^C3O 
O3O300CDt^t>.l^l>-^t^00tDt-COintOCDiniO(NC<l(N-^ 

i-l(Mi-l(NTHCqi-((MrHiMi-i(Mi-iNrH(MrH(Mi-IIMr-(C<Ir-HiM 



























-S 




. . 


u 




■a 
u 


Xi 


'■5 ' 




05 


03 


033 


03= ■ 

^ : 


f^- 


t. 


= ^^ 


g 
1-1 


IU3 

1-; 


■ s 







a 


"o ■ 


al 


p. 


^ 


?? 


) 


a 
O 


u 


a 








•£ 


(3 


c3 



.J-: . • . u~i i-v L~; 1-' U.I QJ 



a^ 



6o 



Correlations of Mental Abilities 



O 

o 

< 
o 



O 

o 



pq 
< 






< cc 

o 



1^ 

o 
o 

o 

03 



X 'eq^Sua'-j 3ni')Buii:tsa 

2 'sq:jauai Suiavbjq; 

X 'smSaa"^ SumBiQ 

2 'spaoj^ Saiiaidtnoo 

X 'spjoj^ Sui^ajduioQ 

X 'sjiBj; 2uinjB3'7 

2 'SUIJOJ |130U?8UIO9f) 

X 'suwoj jBatJ^auioao 

g 'Snippv 

X '3n;ppv 

Z 'saSBBSBj JO jCjoraap\[ 

X 'saSBSSBj JO itjoraajtf 

Z '*sa» V 

X *?S9^ V 

Z 's3:>isoddo itsBg 

X 'sa:jisoddo ^e^a 

g 'spjo^ JO itJ0inaj\[ 

I 'sp-iOj5|\^ JO jtJouiaj\[ 

g 'sa^TsoddQ P-i'BH 

X 'sa:jisoddo P'l^H 

g ''jsaj snBqSniqqa 

X 'ls^:^ snBq3u;qqa 



I T T III T II 

r-HD<N05CO'<l<OrH-*^(NCicOOM0050>0.-i t^-* W 
OOOOO'-lOOOOM'MOO'-'INOINi-iOr-ir-l Tjt 

(M Ot^'*0000Ci:i(N0>M00'^CDTt<OO000>C<3'-l01 ■* 'I' 

III I T IT I I I I I II 1 I 

M P "O 00 U5 t> i-H m -"f -^ P O P .-< ■* rH t^ CO M P (Mt^tO 
i-ii-i.-iCOlMPpPPp.-(pcO(M<NrHINC>p,-( Tji^c^ 

III llTlTlTll II 1 I 

POO>-l<Mi-iOspPCDOiOt^t^.-(t^->*Tt<C»3l> prHi-cM 

C0C0'*PP-*MeCINPCOPC0t^'-l(M'^-*N .-I'-ipiM 

II I I i 

OC0t-05lMI>iMp(M(NP0CP(N>^OC<l00 t^ccMPO 
(N M 05 0? lO C<3 (N P .H .-I P 03 .-I CO IN "-I CO •* (Npi-i,-.r-l 

T)iTtie<icoTt<ooinrHt^05pcsPcoiMP05 oococoPoj--" 

i-H (MCOIM IrHTHi-HC^) i(N(M(NC<H> ■*•<}< M i-i (>) >0 

II II II 

U3 i-l tH Tf p 00 •* rH tC P t)i lO r-( Tfl «D P Ol <N Tf t» 00 0> "-I 
CO<N^ coco rH I T)( I II rHi-l t>. CO .-I (N '-< p P 

II I ' II 

C0lM«PIMrH'*U5t^Pt~PPNC» PPPtHi-iPP-^ 
I --HI 1 |CO>CCO>-l.-iri,_,p f-i(Ni-lN,-|.-lc^lP 

I II I I I I 

cqiH'>i<ir3t~pmi/5co'-H(M-*<Mt- o^tO'^^t^-^Om'-* 

ICOl ■-(•-■■!t<-*'*CO(M OrHC)C>^,-lc^i-*,-(P 

II III II 

(ri-*iOPiO05(NlOiOPC0PP t^CT-^COINi-HW^PP 
■*■*■* Tt* <N ■-( coifs'* CO --It- rt I lMCOW(M(NpP 

I I 

PPPiOiOPC0lO(N'*-<l<00 p(MPtHPOt^oPP<N 
lO-^t^-* rHCOC0-*lMTH l^ i-H I (Ni-lcOCOCOPP 

CO'^pCOpinppiOINOO 00 P 'i' P >CIN 00 1-- to »-< OJ P 

CO CO (N ■* to i-l COt^ r-(INi-l I COP I •-i(N'-H 

I I I I I I I 

c»pi>NPrHiMr-(>n'* cc^cooit^TtippinpXMt- 

COCOiH-^THC^IrH ^^'-t t^i-ICOCO'-l|IMPCO"-'<N<N<N 

I I III I I I I 

t-pT^iOC'lOOiOCDIN TjlNTfOi-ltOPPIMlOTfCOi-iOO 

■-IrHrt I (N.-I I r-ICD rtCOCl-*-*CO^|''-"-<PPPPCj) 

p p OJ CC lO CO •* lO IM lO lO IM lO CO t^ ■* t- IN P Tl< 05 Tf IM 

rH r-( 1-1 rt (M f-l ,H i-< P r-l ■* IC --IH lO | H t-H (M O IZ) p P 

COOOPt-P'^CO lOPiHpiOmiOl.OtHrtpPcolN.-tCO 
IN IN P lO IN IN lO rHiH COCO'^CO'H OCOPPPP 

>H'<JiCOPt^O CO-*lONPC0C<llO'*'*>ONPrtC0PP 
■*Tt(PCOININ lOrt I rH COrtrH | | (NINOPPP 

P(NCOTt<00 P"*CO00rHlOPPPr-IQ000l>O5t^a-*00 
TtllOlOKlTtl (N (N tH tH C^^ rH tH rt | CO CM CO ■* 1 PrH^* 

rtlNrtt- OOOPlOINCDPlOiOt^lNp-^IN'HioOOCOOO 
■*T)C<l<CO Tjt CM IN (N IN Ttl p (N I C0C0lOP(MrtC)CM 

OOCOP t^-^p^-piOlNCOiO tOiOO'^COOINOO'* Oit^ 
CO-^iO COINCO'OrtlrJiTji'^iOI'H CMC>3PC0'HP(N 



I I I 
<NrtlN'HMrt(N'HINrtlNiHCMtHINiHINr-((NiHIN'HC<l 























' 






















) 


Opposites . . 
)ry of Words 
Opposites . . 
i. 




so 

o 

b ^ 


1 


1= I 

— . ci 


leting Words 
ing Lengths, 
lating Length 



03 fl^ 

J2 cj « d •*^ M -O 

w K S w -jj S o; 



^-1 O P w 



Significance of Tests and Analysis of General Intelligence 6i 



o 
o 

o 
iz; 



Pi 






03 



2 ^ 



o 



PM 



X 'sq:^3^^^; Sup-Buipsa 

g 'Sq^3U3''X 3UIAS.13JQ 

X 'si['}3n3T; Suimbjq 

X '^sa:> Bg 
2 'sjjBjj 'Bumxes'^ 
X 'SJIBJ SnrttJBaT; 

Z 'SUUO^J IB0IJ^3tnO8{) 

X 'suuo^i iB0ij:>auio8f) 

Z '3uippv 

X '3nippv 

Z 'sa3'BSSBj; jo jf jouiajf 

X 'S83BSSBJ; JO ^Joraaj\[ 

S ';sa:> V 

X '%'sn V 

g 'e8:>isoddo itsea 

X 's8:);soddo itSBg 

Z 'spjOjVi. JO jtjotnapi 

X 'spjo^ JO Ajoraaj\[ 

2 'sajisoddQ p-i^jj 

X 'sa^TSoddo pJBjj 

Z '%S9% BtiBqSniqqg 

X ';s8^ snuqSuiqqa 



•<tl(MOINOO(N<N-*OOlMOOOSC<5C<ICOa>OSCOOOOCOO 

oO'-^oocO'-l'-^IHT-lc<5co(^^co■-((^4l^50<^)'-^(^^^^^«D 



r-lrHOOirOprHCOOOO'-lpOO'-H>-lO'-l'-< <Sl ^ 0\ 

IT 111 I 



iH CO CO b» O) CO rH i-H cvj o 00 (O O Oi O) 1-1 O 05 05 CO IN CO CO 

— .. H i-l(M ,-H 

I I I I 



OOd5DTl'<MiOmiOOOcDOCOt>-'0'*COTt<000 >-l>-lCvli-i 



I I I 

C0ffll0f005INCTl'-<l(5-<HCD(M«DTt<?qON COOSrtCOCDOS 

■* Tji CO -5t( O Q IM CO CO CO i-H O CO CO O r-i 10 (NOOOi-IO 

T I I 



o^i-<'*.-it^coa>coocoi^o>iOMi-H t^ooi-ioor^coco 

CO (M <N rH CO (N <N <N ■* 00 CO rH rH i-H OS Tj- rt CO CO "-I n CD IM 



Tjl Tf 10 CO i-l ■-( 00 (N (M t-< O CO O :D 10 10 CO 1-H O <M ■*•* 03 
10 10 ■* ■* o CO CO ■* •* <N i-H >-( OS IM rH CO CO to N. O i-IN Ol 



OOJOCOiMOOOCOtOrH CO O 00 1-1 O to CD •* 00 to t^ ■* 50 



to -* 10 1^ (M IM r> i-l O rH o "-H -"tl CO O OS Tj( 00 C (N l^ ^^ IN 
rOCOCO(NTj1TtHiHi-HCO lNC0(Mr-4Q000t<C0'*t0OC3OrH 



tOOOtOOOl C0t01^INOb-i-l0SOt00S(Ml0C0C0M<OiN 
CO'CtOlO'* COlCtO-*tOtOCOW*(NCOOINU5CpiNr-lCO 

COiOi-los OlOlOrHINNOST-loCOt^lNOSl^OST-lTtdOOO 
•*■*■*■<}( •<tl-*IN-*TtltOtOOOM<COi*OOINCOi-lrtO 

tDt^OO OSOa>lO00t^C0-HC0i-it>.r-4Oc0t0t^t0t0O'N 
|--t^00 ■* 10 >0 to 10 IN O CO ■*■* CO -H 10 Tt< IN ■* O i-H "-I O 



CO •*t^lO00-*C0>O-*0S00-*OC0rH-rJHc0OC0-*C0-*IN 
OS 00 1> ■* 10 l> 00 1^ CO ■* 10 ": CO CO IN "O Tt< 10 to .-I CO o o 



'-HINi-IINrtNrHINrHMrHINi-HINr-IIN'HiNiHIN'HINrHIN 





S- 




(US 


IP 






■5 






a 


a 


5 ■ 2 


>1 




a 






h 


"u 
-g 


Ph 


■h5 




2 




Oi 

s 


m" s" 


03 

s 




^ r 


c 




" 




.§' 



1"^ . . LZi '^ i_z!. 'w' »*>' «j «j t:" !/-( 

WWgW<5S<>1OHJp:)0W 



62 Correlations of Mental Abilities 

Probable Ebror of the Pearson Coefficients of Correlation 







.6745 (1— r2) 






{Using the formula, P.E. 


\/n 






Group I, 


Group II, 


Group III, 




n=37 


72^17 


n=20 


r. 


P.E. 


P.E. 


P.E. 


.10 


.11 


.16 


.15 


.20 


.11 


.16 


.14 


.30 


.10 


.15 


.14 


.40 


.09 


.14 


.13 


.50 


.08 


.12 


.11 


.60 


.07 


.10 


.10 


.65 


.06 


.09 


.09 


.70 


.06 


.08 


.07 


.75 


.05 


.07 


.06 


.80 


.04 


.06 


.05 


.85 


.03 


.05 


.04 


.90 


.02 


.03 


.03 


.95 


.01 


.02 


.02 



It will be observed in these tables that the correction for at- 
tenuation cannot be made in certain cases. Such are (i) cases 
(like the correlation between Memory of Passages and Geome- 
trical Forms for the Good group) where the average of the 
raw coefficients, -2i, comes out negative, though the facts for 
the Good and Poor together, and facts found by other workers 
in this field, prove that this inverse correlation is a chance re- 
sult from the small number of cases. Such are also (2) cases 
where either or both of the coefficients of correlation for the 
two trials of the same test are negative, as for instance in Recog- 
nizing Forms and Hard Opposites, the denominator would be 
V-41 X 60. Such negative correlations in the denominator of 
the correction formula are due either to a chance absurdity due 
in turn to the small number of cases, or to facts unrevealed in 
the measures themselves, which make the two trials with the 
same test not a random selection. 

What the true correlations would be if the subjects were 
representatives of people in general, can only be roughly esti- 
mated from the above data. They would of course be lower 
than those given in the top line of the table, and higher than 
those given in the second line, since a normal distribution of 
persons would vary less on the average than those of the amal- 



Significance of Tests and Analysis of General Intelligence 63 

gamated group, and more than the Good group. The true cor- 
relation would probably be considerably higher than that given 
by the Good group separately. If we take the average of the 
correlations given in the second and third lines of Table X, and 
then take the average of this result and that given in the top 
line, we shall probably make as close an approximation to the 
true correlation for people in general as could be arrived at 
from this data. Thus to get the estimated true correlation be- 
tween the Ebbinghaus test and Hard Opposites, take the average 
between 66 and 90, which is 78, and then take the average be- 
tween 78 and 92, which gives us 85 as the estimated true correla- 
tion for a group of normal distribution. The estimated true 
correlations for twelve of the tests of most satisfactory relia- 
bility are given in Table XIV. 



TABLE XIV 
Estimated True Correlation for People in General 

(That is, the probable correlations as they would be if the subjects were 
a very large number of persons representing a random sampling of all peo- 
ple, instead of two small selected groups. This table is compiled from Table 
X as explained above.) 





+3 




CO 






m 

bC 




a 




m 
u 


CO 


03 

+3 
bO 




m 

CO 

o3 


"St 



1 


-4-3 






CO 










bJD 

a 


+3 
be 

a 


a 




f. 





b 


n 




b 


&JD 


u 


c 


^ 


bD 

a 


+3 

c3 




a 


03 



a 


c3 


-1-3 



a 


C 






a 





a 

'+3 




W 


M 


s 


H 


<^ 


§ 


< 





vA 





Q 


w 


Ebbinghaus test 


85 

82 


85 
84 


82 
84 


72 
83 
65 


54 
58 
54 


71 
70 
80 


65 
70 
39 


36 
42 
49 


60 
56 
65 


60 

72 
61 


15 

18 

-05 


33 


Hard Opposites 


95 


Memory of Words 


44 


Easy Opposites 


72 
54 
71 


83 
58 
70 


65 
54 
80 


50 
50 


50 
46 


50 
46 


56 

58 
42 


45 
87 
33 


37 
36 
30 


62 
65 
31 


37 
13 

02 


31 


A test 


99 


Memory of Passages 


29 


Adding 


65 
36 
60 
60 
15 


70 
42 
56 

72 
18 


39 
49 
65 
61 
-05 


56 
45 
37 
62 
37 


58 
87 
36 
65 
13 


42 
33 
30 
31 
00 


30 
39 

77 
0? 


30 

36 

38 

98 


39 
36 

44 
-0? 


77 
38 
44 

07 


02 

28 

-02 

07 


00 


Geometrical Forms 


16 


Learning Pairs 


51 


Completing Words 


05 


Drawing Lengths 


96 


Estimating Lengths 


38 


'?5 


44 


31 


?9 


?9 


00 


16 


51 


05 


96 




Totals 


633 


663 


618 


588 


550 


484 


478 


440 


452 


522 


141 


989 









64 



Correlations of Mental Abilities 



For the remaining two tests, Recognizing Forms and Scroll, 
it is somewhat less safe to venture an assertion as to the prob- 
able true correlations with each of the other tests. As has 
been stated above, the ordinary methods of correction cannot 
be applied on account of the low reliability of the tests them- 
selves. The average of the correlations Rp-^q^, Rpiq2> ^p2Qi> 
Rp^q^y that is, the numerator of the correction formula, gives 
us on the whole a result considerably less than the raw coeffi- 
cient, which is itself too small. I have calculated the probable 
true correlations between the Scroll test and the Recognizing 
Forms test, with each of the other tests, in the same way as in 
Table XIV, except that they are calculated on the basis of the 
raw coefficients instead of the correlated coefficients. The re- 
sults are: 





-ij 










ro 




m 

a 




XD 

a 








bC 




m 
m 

CD 

3 




1 

o 


O 
P, 




O 




o 

E^ ■ 


Ph 


Ph 
c 




a 


C 


>3 

bC 

a 




-a 


o 


b 


n 




b 


b/D 






a 






bC 

a 


'-13 




g 
IB 


t3 


o 


>> 


CO 

CD 


o 

a 


a 


a 

o 


a 


WJ 

o 


'o 


a, 


% 


a 




^ 


1°^- 




crt 


' 




TJ 


a> 


<D 


a> 






i-> 






W 


w 


1^ 


W 


< 


% 


-< 


O 


h-1 


rt 


02 


o 


P 


w 


Recognizing Forms . . 


65 


45 


48 


42 


28 


38 


31 


32 


41 




17 


30 


32 


18 


Scroll test 


35 


32 


27 


22 


22 


33 


42 


11 


20 


17 




20 


11 


09 



They are probably at least lo per cent too low, but I leave 
them as they are, as they are uncertain at best with my data. It 
will be seen, however, that the Scroll test correlates much less 
highly with the other tests than does Recognizing Forms, in 
spite of the fact that on account of its greater reliability, the re- 
sults as given are less attenuated by chance errors. 

As is shown in Table XIV the order in which the different tests 
(exclusive of Recognizing Forms and Scroll) correlate with the 
other tests is : Hard Opposites, Ebbinghaus, Memory of Words, 
Easy Opposites, A test. Completing Words, Memory of Pas- 
sages, Adding, Learning Pairs, Geometrical Forms, Estimating 
Lengths, Drawing Lengths. 



Significance of Tests and Analysis of General Intelligence 65 

3. Grouping of the tests according to relationships shown by 
the correlation coefficients 

(i) Tests of selective thinking 
Table XIV, Estimated True Correlations, shows us that the 
correlation between the Ebbinghaus test and Hard Opposites is 
85. This high correlation suggests that we are not far wrong 
in classing these tests together as we have done in calling them 
both tests of selective thinking. In fact this correlation is al- 
most as high as the correlation between the first and second 
trials of each test. 

(2) Memory tests 

We see also that the correlation between Memory of Passages 
and Memory of Words is 80. On this basis we are justified in 
classing them together as memory tests, implying that they test 
in large measure the same ability. 

(3) Association tests 

It would appear, however, that we would not be justified in 
grouping Adding and Easy Opposites together as tests of asso- 
ciation in the sense of implying that they both are tests of the 
same thing. The correlation between them is only 56, not 
nearly as high as is the correlation between Easy Opposites and 
the tests of selective thinking, particularly Hard Opposites 
which is 83. The fact is that the Easy Opposites test is a test 
of selective thinking, especially for the Poor group. 

The Completing Words test is correlated more closely with 
Adding than with any other test, yy; the correlation between 
Easy Opposites and Completing Words is 62. 

Learning Pairs does not correlate closely with Adding, Easy 
Opposites or Ba and so cannot be classed with them as a test 
of the same kind of thing. 

(4) Perception tests 

On the other hand, the correlation between A test and 
Geometrical Forms is 8y, being very much higher than the cor- 
relation of either test with any other test. Hence our justifica- 
tion in grouping them. 



66 Correlations of Mental Abilities 

(5) Motor control 

The Scroll test has turned out to be quite unsatisfactory as 
to reliability in the case of the Good group. If we assume that 
it gives us satisfactory results in the case of the two groups com- 
bined, and in the case of the Poor group by itself, the co- 
efficients of reliability being 76 and 71 respectively, we could on 
this basis estimate the degree of its relationship to the other 
tests, and to General Intelligence. Just to what extent ability in 
this test is significant of other sorts of motor ability, we are of 
course unable to say. 

(6) Discrimination of lengths 

The estimated true correlation between Drawing Lengths and 
Estimating Lengths is only 26. In making this statement, how- 
ever, we should add that the figures are relatively untrust- 
worthy on account of the low reliability of the tests themselves, 
particularly Estimating Lengths, making the correction formula 
scarcely applicable. However, the very considerable differences 
between the correlation of random halves of the same test with 
each other, and the correlation of the two tests with each other, 
make it clear that there are very appreciably different factors 
involved in the two tests as given. 

4. Order in which abilities correlate with other abilities tested 
In order to determine which of the tests correlate most highly 
with other tests, we have simply to sum up the totals of the 
columns given in Table XIV. The average correlation of each 
test with the eleven other tests is : 

Hard Opposites 60, Ebbinghaus test 58, Memory of Words 
56, Easy Opposites 53, A test 50, Completing Words 47, 
Memory of Passages 44, Adding 43, Learning Pairs 41, 
Geometrical Forms 40, Estimating Lengths 26, Drawing Lines 
13. On the basis of our separate estimate, the figures for Recog- 
nizing Forms and Scroll would be 41 and 26 respectively. 
Grouping the related tests we have: 

Average correlation of Selective Thinking with other 

tests 59 

Average correlation of Memory with other tests 50 



Significance of Tests and Analysis of General Intelligence 67 

Average correlation of Association (exclusive of Learning 

Pairs) with other tests^ 48 

Average correlation of Perception with other tests 45 

Average correlation of Motor Control with other tests . . 26 
Average correlation of Discrimination of Lengths with 

other tests 19 

Provided only we have appropriately named the abilities 
above mentioned, all this means that, using the argument from 
correlation alone, power of selective thinking is more intimately 
connected with, and more characteristic of, general mental 
ability than is any of the other abilities tested ; that memory is 
next most highly correlated with general ability; the simpler 
forms of association next; perception next; motor control con- 
siderable less; and discrimination of lengths least of all. This 
confirms the more direct argument stated above, from the ex- 
tent of overlapping of the Good and Poor groups in the different 
tests. 

5. Analysis of the individual differences revealed by the tests 
and evidence that they are largely due to differences 
in native mental capacity 

We are now in a better position to analyse the differences 
between the two groups that are revealed by the tests, and to 
indicate to what they are due. The most obvious difference 
between the two groups of persons is of course a difference in 
efficiency. That the members of the Poor group were relatively 
inefficient is shown by the nature of their previous employments, 
and by the fact that all but two of them were out of regular em- 
ployment. On the whole it is the more inefficient ones who are 
the first to be thrown out of employment. While an occasional 
one loses a good position owing to some bad habit such as in- 
temperance, dishonesty, etc., the many lose their positions owing 
to lack of initiative and zeal, stupidity, inability to make them- 
selves so useful that they cannot be easily replaced if dis- 
missed ; in short, through general lack of efficiency. Moreover, 
not one of these persons, with a possible exception of No. 18, 
the brakeman who was then assistant manager of the Salvation 
Army Industrial Home, had ever held a position calling for 



^ Including Learning Pairs, 46. 



68 Correlations of Mental Abilities 

much exercise of intelligence, though they had reached years of 
maturity. The median age was 36, ranging from 23 to 52. As 
to the amount of schooling they had had, there was considerable 
divergence, the median number of years schooling being 7 and 
ranging from i to 12. With regard to those who had a small 
number of years' schooling it is safe to assume that in a rather 
large proportion of cases inability to get on well at school had 
a good deal to do with it. On the basis of these facts it seems 
clear that the twenty members of the Poor group represent a 
grade of intelligence and mental capacity very far below the 
average. 

In the opinion of the writer, who spent from four to six 
hours with each of them and had an excellent opportunity to 
judge the characteristic methods of each in attacking mental 
difficulties, it is practically certain that at least fifteen of the 
twenty represent that quality of mind which ranges from some- 
what below the average in mental capacity to that which is only 
slightly above the feeble minded. They represent persons who, 
on the whole, are not at all bright, even if not positively dull 
in school; who have no particularly strong interests or am- 
bitions, and who are likely on leaving school to follow the line 
of least resistance in earning a living, doing most things they 
attempt with indifferent or poor success. They represent the 
kind of person relatively lacking in foresight, energy, self-re- 
liance, and all round mental capacity; the person likely to suc- 
ceed fairly well only if well directed and especially trained in 
some particular line of work, but who, under the most favorable 
conditions possible, is utterly incapable of attaining a degree of 
achievement much beyond mediocrity. At least six of these 
were persons considered dull by their acquaintances. As to the 
remainder of the group, in the opinion of the writer, they repre- 
sent persons ranging in mental capacity from that of the fifteen 
described above to something above the average in the case of at 
least one or two. 

The Good group, on the other hand, is composed of persons 
who are far above the average in mental capacity. It is safe 
to say that persons who become college professors or instructors 
before the age of thirty-five possess mental ability ranging from 
considerably above the average toward the very highest mental 



Significance of Tests and Analysis of General Intelligence 69 

capacity. That the members of the Good group are representa- 
tive of mental ability far above the average is evidenced by the 
nature of the positions they now hold. Eight or nine of the 
seventeen at present occupy college or university positions. The 
rest hold educational positions, mostly in normal schools of high 
rank, with the exception of one, who holds an important and 
responsible position in a philanthropic organization. There can 
be no reasonable doubt, therefore, that the two groups are repre- 
sentative of very decided contrasts of mental ability. 

One may say that the qualities making for success are in 
large part moral — capacity for self-control, self-denial, indus- 
try, conscientiousness, etc. Some of these qualities or tendencies 
are such as to be indicated to a close observer, in the way in 
which the mental tests were attacked. Analysis would un- 
doubtedly show positive correlation between mental and moral 
qualities. In addition, one of the most striking differences be- 
tween the two groups was a decided contrast in attitude with 
regard to time. All of the Good group did the tests with a 
high regard for the value of time, while such a thing as the 
time element being of much significance or importance hardly 
seemed to dawn upon members of the Poor group, even though 
the instructions given were the same for both groups. 

Having considered group differences on the basis of general 
principles, let us now consider the differences in the two 
groups as revealed by the tests. As above stated, page 53, the 
most decided difference between the groups is in the tests of 
selective thinking — Ebbinghaus test and Hard Opposites. This 
is exactly what the results obtained in investigations on the men- 
tality of the feeble minded would lead us to expect. All of 
those who have worked with the feeble minded agree that they 
are farthest removed from the normal in ability to deal with the 
abstract, ability to get and use meaning and significance. It is 
also demonstrated that the most painstaking educational efforts 
to improve their capacities in this respect are relatively ineffec- 
tive.^ The same would undoubtedly hold true, though to a less 
degree, of persons somewhat above the mentally defective. 

It may perhaps be objected that the two tests in question are 
simply language tests, and, as such, measures of amount of train- 



^ See Goddard, Journal of Educational Psychology, November, 1911. 



70 Correlations of Mental Abilities 

ing and education rather than measures of mental capacity. 
That this is not the case is evidenced by the low correlation be- 
tween number of years schooling and rank in the tests. The 
correlation between number of years schooling and rank in the 
eight tests correlating most highly with other tests is 38. This 
amount of positive correlation could be accounted for on the 
basis of the correlation between mental ability and staying on 
at school. Studies in retardation have shown that a considerable 
proportion of those who leave school at an early age, do so be- 
cause they are relatively unable to do the mental tasks required 
of them in school. In other words, in a considerable propor- 
tion of cases, a small number of years schooling means inability 
to learn advanced and difficult language work, rather than 
lack of opportunity to learn it. There is no way of calculating 
directly the correlation between general intelligence in the Poor 
group, and rank in the tests of selective thinking, as we have 
no way of independently ranking them in general intelligence. 
In the Good group, however, the correlation between estimated 
intelligence and rank in the tests of selective thinking is 92.5. 
In the Poor group it would probably be higher still as in general 
all other correlations are. Hence the tests of selective thinking 
do not measure mere training and schooling. 

This was further evidenced by a consideration of individual 
cases. In general those who were considered decidedly dull or 
stupid by their fellows, did poorest in the tests of selective 
thinking. 

Moreover, language tests similar to those here given are not 
unfair tests of ability as opposed to mere education, since the 
intelligence of a primitive people can be gauged by the language 
they find it necessary to evolve and use. Feeble-minded chil- 
dren are, on the whole, decidedly deficient in acquiring higher 
forms of language, while bright children with similar educational 
advantages, acquire language naturally and easily. It is the same 
with many of the Poor group. Their low grade of native 
mental ability has made them very slow to acquire average 
facility in the command of the higher form of language, and 
very difficult for them to acquire and make use of abstractions, 
fine shades of distinction in the meaning of words, etc. These 



Significance of Tests and Analysis of General Intelligence 71 

differences in native capacity come out in any classroom of an 
elementary school. 

In a certain sense all ability is dependent upon training and 
practice inasmuch as one cannot long retain a capacity unless 
it is more or less exercised. The skill of the talented musician 
could not be achieved without attention given to music. But 
a true way of viewing the difference between a musical genius 
and a person of average musical ability is just this : The in- 
terest and inborn capacity of the one is so great that it leads him 
to get abundance of practice and training in the capacity, where- 
as the weaker interest and inborn capacity of the other leads 
him to let the practice of other abilities and capacities predomi- 
nate. So with interest in, and ability to deal with the abstract. 
Gifted minds early become interested in mental exercises of a 
kind for which the dullard has no interest. Interest in fairy 
tales, romance, fiction, literature, science and philosophy, in so 
far as these involve the use of concepts, would lead to the ex- 
ercise and development of the higher forms of association and 
abstraction. In short, we may well look to language tests in 
some form, to furnish good tests of general intelligence. 

Moreover, the high correlations within the Good group itself, 
where there has been presumably no appreciable inequality on 
the basis of opportunity for education, further substantiate the 
view that by far the most influential factor in making for effi- 
ciency in these tests, is the native capacity of the individual in 
question, and not simply his training and environment. The 
results in memory and association show nearly as much dif- 
ference between the two groups as do the tests of selective 
thinking, and the same general line of argument would hold 
with regard to them. 

To test still further the extent to which ability in certain of 
the tests is significant of general intelligence as commonly under- 
stood, there was taken for each individual a combined measure 
obtained by summing up his score in the Ebbinghaus test, Hard 
Opposites, Easy Opposites, Learning Pairs, and Recognizing 
Forms, arranged in such a way as to allow approximately equal 
weight to each test. The scores of the different subjects, in 
terms of the deviation from the median of all are: 



72 Correlations of Mental Abilities 



ibject 


Deviation 


Subject 


Deviation 


1 


89 


18 





2 


61 


19 


—2 


3 


95 


20 


—15 


4 


49 


21 


—26 


5 


70 


22 


—9 


6 


43 


23 


—26 


7 


39 


24 


—27 


8 


54 


25 


—31 


9 


59 


26 


—25 


10 


21 


27 


—13 


11 


53 


28 


—16 


12 


44 


29 


—32 


13 


42 


30 


—59 


14 


25 


31 


—45 


15 


49 


32 


—51 


16 


47 


33 


—119 


17 


21 


34 


—54 






35 


—59 






36 


—73 






37 


—127 



There is no one of the Poor group who reaches the lowest 
one of the Good group; in fact there is a decided gap of 2i 
here. There is a much larger gap between the median of the 
Good group and the highest one of the Poor group, namely, 49. 
Thus we see how effective such a combined score is in separat- 
ing the Good group from the Poor. 

TABLE XV 







Ranks of Good Group 


FOR 


Imputed 


Intelligence 






■s 


e 


^0 


50 


'e 


fti 


•<~.. 


Cn 


-se 


'?*> 


•c~« 


-« 




S 






X2 


^ 


^ 


>> 


>> 


SI 


J2 




>> 


>. 

^ 




>> 






"0 
6 

12; 


P5 


0. 




1 

P^ 




bC 


bO 
PI 


1 


P^ 


be 

1=1 

P5 


bC 

a 
1 

P^ 


bC 




« 
-5 

0) 


7 


7 


6 










15 








7 


6 


11 


7 


8 


6 


5 


6 


6 


5 


11 


9 




3 


9 


6 


5 


5 




3 


2 


1 


2 


7 


2 


6 


6 


2 


4 


7 


3 


2 


3 


3 


12 


10 


9 


5 


8 


7 


7 




9 


13 


10 


11 


12 


8 


9 


6 


8 












11 




14 




9 








5 


5 


4 


7 


3 


3 


12 


5 


8 


7 


8 


4 


4 






16 


15 




8 






10 


16 




15 




15 






15 


13 


12 




9 


9 


6 


9 


7 


5 


5 


4 


14 


9 


6 


8 


2 


3 


3 


3 


4 


4 


3 


3 


4 


6 


3 


5 


7 


4 


4 


10 


16 


11 


10 


11 


10 


13 


14 




11 




16 




12 


11^ 


9 


9 


10 




13 


9 


4 


4 


7 


9 


6 


10 


10 


9 




11 


11 




12 


10 






12 






11 


13 




10 


11 


17 


17 




11 


12 


11 


14 


13 


10 


12 


8 


17 


11 


13 


12 


14 


14 


8 


13 


2 


8 


8 


8 


6 


8 


5 


12 


8 


7 


8 


4 


4 


2 


4 


5 




2 


2 


3 


2 


2 


2 


3 


2 


2 


1 


1 




1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


15 


13 


7 








5 


10 








8 






8 



Significance of Tests and Analysis of General Intelligence 73 



To further test the extent to which such a combined score is 
a measure of ' general intelligence,' the individuals of the Good 
group were rated in order of merit for general intelligence each 
by the rest of the group, so far as was possible, four years after 
the tests were taken. The rankings, including two rankings by 
the experimenter, made a month apart were as shown in 
Table XV. 

Taking the individuals who were ranked by ten or more 
persons, and using for each two random halves of his ranks, and 
all together, we have the following: 











S-t 
















<a 
















M 








+s 


-fj 


CM 











^ 

^ 


0) 


<o 


-s 


73 


-u 


«n 


"3 


In 


J2 


J2 


t— 1 


(M 


oi 




.£J 





3 


'0 


>> 








T3 

PI 


4^ 


d 


6 


a 





a 

P4 


A 


A 


A 


















P.E. 


P.E. 


P.E. 


1 ranked above 4 by 100% 


100% 


100% 


3.5 


3.5 


3.51 


4 


3 ' 


50 


66.6 


58 





.64 


.30 


3 


2 ' 


50 


82 


66.6 





1.36 


.64 


2 


5 ' 


66.6 


66.6 


66.6 


.64 


.64 


.64 


5 


8 ' 


66.6 


80 


73 


.64 


1.25 


.91 


8 


13 ' 


66.6 


75 


73 


.64 


1.00 


.93 


13 


14 ' 


66.6 


66.6 


66.6 


.64 


.64 


.64 


14 


9 ' 


50 


83.3 


66.6 





1.43 


.64 


9 


12 ' 


40 


83.3 


64 


— .38 


1.43 


.53 


12 


10 ' 


100 


80 


89 


3.5 


1.25 


1.82 


10 


17 ' 


100 


80 


89 


3.5 


1.25 


1.82 



^ Inferring from the percentages the distances between the individuals 
in question in terms of the P.E. by means of the following table quoted from 
page 16 of "The Perception of Small Differences" by Fullerton and Cattell. 



7or 


P.E. 


%r 


P.E. 


%r 


P.E. 


%r 


P.E. 


%r 


P.E. 


50 


.00 


60 


.38 


70 


.78 


80 


1.25 


90 


1.90 


51 


.04 


61 


.41 


71 


.82 


81 


1.30 


91 


1.99 


52 


.07 


62 


.45 


72 


.86 


82 


1.36 


92 


2. 08 


53 


.11 


63 


.49 


73 


.91 


83 


1.41 


93 


2.19 


54 


.15 


64 


.53 


74 


.95 


84 


1.47 


94 


2.31 


55 


.19 


65 


.57 


75 


1.00 


85 


1.54 


95 


2.44 


56 


.22 


66 


.61 


76 


1.05 


86 


1.60 


96 


2,60 


57 


.26 


67 


.65 


77 


1.10 


87 


1.67 


97 


2.79 


58 


.30 


68 


.69 


78 


1.14 


88 


1.74 


98 


3.05 


59 


.34 


69 


.74 


79 


1.20 


89 


1.82 


99 


3.45 



74 



Correlations of Mental Abilities 



Calling the degree of ability midway between subject No. 8 
and subject No. 13 the central tendency, we get Table XVI. (A 
case of 100 per cent is treated as equivalent to 3.5 P. E. because 
there is a high probability that with many judges the lOo's in 
these results would fall to 99 or even much lower.) 

TABLE XVI 

Deviation Measures Inferred from Per Cents op Judgments 
OP Superior 





Deviations 


Deviations 


Deviations 




No. of 


from Median, 


from Median, 


from Median, 




Subject 


1st half 


2nd half 


entire set 




1 


5.1 


7.9 


6.5 




4 


.60 


4.39 


2.94 




3 


1.60 


3.75 


2.64 




2 


1.60 


2.39 


2.00 




5 


.96 


1.75 


1.36 




8 


.32 


.50 


.45 




13 


— .32 


— .50 


— .46 




14 


— .96 


—1.14 


—1.10 




9 


— .96 


—2.57 


—1.74 




12 


— .58 


—4.00 


—2.27 




10 


—4.00 


—5.25 


—4.09 




17 


—7.5 


—6.50 


—5.91 





Using this deviation table, the coefficient of correlation cor- 
rected for attenuation was calculated between ' general intelli- 
gence ' as judged by one's fellows, and the record secured in the 
five combined tests. This correlation is 92. 

In order to test the reliability of this combined score, the co- 
efficient of correlation was calculated between the combined 
score for the first trials, and the combined score for the second 
trials. For the Good and Poor subjects together the raw co- 
efficient is 96; for the Good group (12 subjects only), 72; and 
for the Poor, 90. This high reliability of the combined score 
proves that fifty minutes or so spent in getting such a record, 
gives us a good measure of whatever it is that this combined 
score measures. That this, in turn, gives us a very significant 
indication of the general mental ability of the individual in ques- 
tion, is shown by the almost perfect correlation between score- 
in-the-combined-tests and estimated intelligence. 

Again the Pearson coefficients of correlation corrected for at- 



Comparison of Results With Those of Other Investigators 75 

tenuation were calculated between Estimated Intelligence and 
each of the eleven most reliable tests. The coefficients are : 



Estimated Intelligence and Hard Opposites . 
Ebbinghaus test. 



96 
89 
93 
35 

82 
72 
34 



Memory of Words 

Memory of Passages 

Easy Opposites 

Adding 

Learning Pairs 

Completing Words (?) 100^ 

A test 21 

Geometrical Forms 07 

Drawing Lengths — 20 

(These coefficients are calculated of course on the basis of only twelve of 
the Good subjects.) 

Here again is indicated how reliable as tests of intelligence 
are the Ebbinghaus test, Hard Opposites and Easy Opposites. 
The order in which the different capacities correlate with gen- 
eral intelligence is practically the same as shown in Table XIV, 
and further substantiates the results there stated. 



VII. Comparison of Results With Those of Other In- 
vestigators 

One of the earliest attempts to give an exact quantitative 
statement of mental relationships was that of Wissler ('01). 
The correlations obtained by Wissler, however, are on the whole 
much too low, owing largely to the fact that about twenty dif- 
ferent capacities were tested in less than fifty minutes, making 
the measure of each person's capacity in each trait altogether in- 
adequate. It is impossible on the basis of Wissler's data to es- 
timate how much the correlations he found would be raised by 
correction for attenuation due to inaccuracies in the measures 
themselves. 

In the case of the correlations obtained by Aikens and Thorn- 
dike ('03), also, the absence of data makes it still impossible to 
estimate how much they are influenced by attenuation. Impor- 
tant later studies demand detailed consideration. 

Nors worthy ('06) compared mentally defective children with 
normal ones by the use of tests similar to those here used. The 
mental capacities tested were: i, Ability to form abstract ideas 

^ Not sufficiently reliable; as the reliability coefficients of the completing 
words test in the Good group is only 27. 



76 



Correlations of Mental Abilities 



(recognition of nouns) ; 2, Ability in appreciating relationships 
and in controlled association (part-whole test, genus-species, 
easy opposites) ; 3, Memory (words and sentences) ; 4, Ac- 
curacy and speed in Perception (A test and a-t test) ; 5, Percep- 
tion of weight (accuracy in judging relative weights) ; 6, Motor 
control (maze and form board). Numbers i and 2 are com- 
parable with our selective thinking and association tests, number 
5 is probably somewhat akin to accuracy in judging lengths, and 
the maze test in number 6 is very similar to our scroll test. 

Miss Norsworthy found that the defectives were farthest 
removed from normal children in ability to deal with abstract 
data. This is shown in the following table, compiled from re- 
cords of about 137 cases, ranging in age from eight years up : 



% above 

median 

for 

ordinary 
children 



% above 
— 1 P.E. (or 
lowest 25% 
of ordinary- 
children) 



% above 
—2 P.E. (or 
lowest 9% 
of ordinary- 
children) 



1. Height 

2. Weight 

3. Pulse 

4. Temperature 

5. Weight test 

6. A test 

7. a-t test 

8. Memory of unrelated words . . 

9. Composite of 5, 6, 7 and 8 . . . 

10. Dictation 

11. Memory of unrelated words. . 

12. Part-Whole test 

13. Genus-Species test 

14. First Opposite test 

15. Second Opposite test 

16. Composite of 13, 14, 15 and 16 



45 

44 

49 

26 

18 

9 

1 

6 

1 

10 

5 

9 

9 









61 
66 
69 
59 
28 
18 
14 
18 
15 
10 
19 
17 
16 

0. 

1 

1 



77 
77 
86 
77 
39 
34 
28 
27 
27 
21 
30 
27 
17 
5 
7 
10 



According to her results, the order in which the different 
abilities tested would correlate with intelligence is roughly as 
follows : abstraction and association ; memory ; various forms 
of perception ; motor control. This agrees with our results in 
so far as they can be definitely compared. Miss Norsworthy's 
tests of abstraction and association would seem to be very 
similar, and to require almost equal powers of abstraction ; 
hence the somewhat higher rank relatively of association as com- 
pared with our results. Abstraction is of course a relative term. 



Comparison of Results With Those of Other Investigators 7 7 

What would be severe trials of abstraction to a feeble minded 
person, or to an immature mind, might be mere tests of rapidity 
and ease of association and memory to an abler or more mature 
person. As we stated elsewhere, the Easy Opposites test tO' 
many of the Poor group, was like the Hard Opposites test for 
the Good group. 

Lewis M. Terman ('06) tested seven of the brightest and 
seven of the dullest boys of a group of five hundred elementary 
school pupils. The capacities tested were: 
Powers of Invention and Imagination as tested by ability to 

solve mental puzzles. 
Logical Processes as te:sted by solution of problems in arith- 
metic and other problems requiring original thinking. 
Mathematical Ability as tested by problems requiring the 

more mechanical phases of arithmetic. 
Mastery of Language as shown in word building, reading, 
Ebbinghaus Mutilated Text, spelling and facility in inter- 
preting commands. 
Insight as shown in the interp;-etation of fables. 
Ease of Learning the game of chess. 
Memory of geometrical figures, chess moves, a story read, and 

the solution of a mechanical puzzle. 
Motor Ability, as shown in learning visual-motor coordina- 
tions, skill in running down stairs, and in carrying a book 
on the head. 
Terman concludes that the bright boys are superior to the dull 
in all the mental tests, and inferior in the motor. This su- 
periority of the dull group in motor tests, if characteristic of 
persons in general, would of course mean a negative correlation 
between motor ability and " intelligence," and be in conflict with 
our conclusion of a small but positive correlation. It is cer- 
tain, however, that at least a part, and probably all, of this 
superiority of the dull group in motor ability was due to greater 
maturity on account of their being on the average 12.7 months 
older than the bright group. Again, it may be, in part, that 
boys in school who have some motor ability and interest in that 
kind of thing, are on that account more likely than other boys 
to give little attention to linguistic and abstract studies, and for 
that reason are likely to be considered less intelligent by their 



78 



Correlations of Mental Abilities 



teachers than they really are, and duller than boys who lack 
such interests altogether. The fact that the dull boys all pre- 
ferred games and the bright ones reading also suggests this con- 
clusion. On general principles it seems hardly likely that there 
should actually be a negative correlation between motor ability 
and intelligence, at least as far as native capacity is concerned. 
It would seem quite probable, too, that the groups here selected 
would not represent bright and dull children respectively as 
judged from a more general point of view than that of a school 
teacher. 

I have calculated the Pearson coefficient of correlation for 
each test with every other test, using Terman's scores for each 
of the fourteen boys taken all together in one group. In order 
to bring out the relationships between the different tests as fully 
and accurately as possible, I have taken the actual scores made 
instead of the ranks. The only exception to this was in the case 
of the ' Interpretation of Fables,' where on account of the omis- 
sions it was not very practicable to take the scores. The co- 
efficients are given in the table below. 

















m 


















o 




































-O 


















rf 


















fe 












m 






.l , 












ai 






o 










CO 


CQ 
O 

o 
o 












o 




"S 


p^ 




a 


cj 


Si 




c3 





a 


o 


o 

s 


'-2 
c 


0) 


< 

Li 

o 




c3 

1-5 


6 


§ 


o 




c 

>—< 


CI 


o 


Language 




81 


86 


75 


78 


72 


66 


—36 


Chess 


81 

86' 

75 


82 

77 


82 
73 


77 
73 


65 
74 
62 


78 
64 

58 


62 
70 
63 


—23 


Mathematics 


—48 


Logical Processes. 


—22 


Memory 


78 


65 


74 


62 




58 


72 


— 26 


Invention 


72 
66 


78 
62 


64 
70 


58 
63 


58 
72 


36 


36 


— 14 


Fables (interpretation of) . 


—52 


Motor Ability 


—36 


—23 


—48 


—22 


—26 


—14 


—52 










422 


422 


401 


386 


383 


350 


317 


— 221 



The table gives of course the raw coefficients, and correction 
for attenuation would raise them somewhat. 

On the other hand these fourteen boys, like our thirty-seven 



Comparison of Results With Those of Otlier Investigators 7 9 

men, represent a selection half from near the top and half from 
near the bottom of the scale of general intelligence. In so far 
forth the correlations are too high. They should be thought of 
much as the raw correlations for the Good and Poor together 
in our own experiment. The high intercorrelation (with the ex- 
ception of the motor tests where the negative correlation in evi- 
dence has already been accounted for) are in harmony with our 
results. 

W. C. Bagley ('01) reported a negative correlation between 
motor skill and intellect. Professor E. L. Thorn dike^ has shown 
that this result was due to an arithmetical error, and to over- 
sight of the influence of the age factor. When children of 
nearly the same age are taken, Bagley's data give a slight posi- 
tive correlation between mental and motor ability. 

Binet ('99) has attempted to differentiate intelligent pupils 
from unintelligent by the use of tests of voluntary attention. 
He considers that the tests he used are not, properly speaking, 
tests of comprehension, but depend upon processes relatively 
more simple, — especially acts of memory and comparison. He 
tested eleven subjects, five intelligent and six unintelligent. The 
tests included accuracy in tactile sensibility; quickness of re- 
action time ; speed and accuracy in counting dots ; perception of 
change in the rate of speed of rhythmic movement; counting of 
rhythmic sounds ; copying figures, different varieties of sen- 
tences and drawings; rapidity of perception of words and 
figures seen for a fraction of a second; accuracy and speed in 
picking out one or more letters from a printed page (our A test 
and an extension of it) ; and simultaneous adding. 

Binet found that a number of the tests did establish a clear 
dift'erentiation between the bright and the dull pupils, and that 
they are therefore promising as tests. Those which turned out 
to be the best in this respect he found to be the tests of accuracy 
in tactile sensibility, counting rhythmic sounds, copying figures, 
sentences and drawings, memory of figures, and cancellation of 
letters. He found also that this difference is most marked at 
the first trials, but diminishes with subsequent trials, and that 
in some cases it may be effaced. On account of the small 
number of Binet's subjects, and on account of the fact that, sev- 

^ Educational Psychology, 1903 edition, pp. 148, 149. 



8o 



Correlations of Mental Abilities 



eral of the tests being new, the subjects' records are hard to 
evaluate with accuracy, it is unsafe to make very specific com- 
parisons. However, subject to these hmitations, the group dif- 
ferences brought out by the tests are shown in the two following 
tables. Table XVIII gives a comparison of the average per- 
formance of the bright group with that of the dull, on the basis 



TABLE XVII 



Bright 



Dull 



Tactile perception, errors with points 2 cm. apart. . . . 

Counting of dots, errors in score 

Counting of sounds, errors in score 

Copying figures, average number 

Memory ; numbers forgotten in 5 numbers of 5 figures 
Reading through an opening, errors (Rapidity of 

Apperception) 

Simultaneous adding, errors 

Cancellation of- letters, errors 

Simple reaction time 



20% 
3.4% 
4.3% 
3.6 


54% 
5% 

20% 
2.8 


12 


42 


34 


34.5 


19% 
9% 
24 


23% 

27.5% 

24% 



TABLE XVIII 

Ranking of Pupils in the Different Tests 















d 




















o 




















HJ 




2 


lU 














Oh 


fcX) 


(D 


a 














Ol 


PI 


+^ 




»>5 




'3 






S-i 


TS 


■s 


H 




IS 


o 




o 


CD 

i 




ft 


< 


1-1 


P! 
_0 




03 


•IH 


'^H 


bD 






j3 


p; 


S 




PI 


o 


O 


fe 




o 


o 


o 


''^ 


to 
o 




.s 


■-3 


g' 


o 


-3 




rS 


P5 


.^ 




c 


Pi 


>^ 


a 




^ 


o 


a, 


-§ 


o 

03 


o 


:3 
o 


O 


^ 


S 




a 


m 


H 


o 


O 


Q 


S 


rt 


xn. 


o 


m 


A 


1 


7 


1 


3 


5 


3 


2 


2 


6 


B 


1 


2.5 


3.5 


1 


1 


4 


1 


4 


7 


C 


3 


2.5 


3.5 


2 


4.5 


6.5 


6 


5.5 


8 


D 


6 


7 


3.5 


8.5 


9 


6.5 


3 


5.5 


9 


E 


3 


7 


2 


6 


6 


8.5 


4 


7 


1 


F 


6 


2.5 


8 


11 


11 


8.5 


5 


2 


2 


G 


6 


5 


5 


10 


2.5 


1 


5 


2 


2 


H 


8 


10 


9 


4 


4.5 


2 


7 


10 


10 


I 


9.5 


2.5 


10 


5 


7.5 


5 


10 


5.5 


5 


J 


9.5 


9 


6 


8.5 


10 


10 


9 


8.5 


3.5 


K 


3 


9 


7 


8.5 


7.5 


11 


8 


8.5 


3.5 


No. of group 


1 


3 





2 


2 


3 


1 


2 


4 


displacements. 





















Comparison of Results With Those of Other Investigators 8i 

of the first trial of the test only, in order to rule out the factor 
of mental adaptation through practice. 

Binet lays great stress upon the conclusion that the difference 
between the intelligent and the unintelligent consists in quick- 
ness of adaptation. The bright pupils adapt themselves more 
quickly than the dull; the dull adapt themselves in turn, but 
more slowly. In so far as this were true, other things being 
equal it would imply, with reference to correlations between 
different tests, that they should be relatively high with unprac- 
ticed subjects, and would gradually diminish as the subjects had 
more and more practice. 

Spearman and Krueger in working over Oehrn's results from 
ten subjects, including five medical doctors and three medical 
students, found that up to a certain point correlations increase 
in size as practice increases, and that after that point they again 
tend to diminish. The decrease in this case may be due to 
fatigue entering as a disturbing factor as the test is prolonged. 
The change in the size of the correlations as practice proceeds 
is shown in the following table. 



TABLE XIX 

Uncorrected Coefficients of Correlation for Each Successive 
Quarter Hour, According to the Results of Oehrn 



Quarter Hour 



Writing and Adding 

Writing and Counting 

Writing and Reading 

Writing and Learning by Heart . 

Adding and Counting 

Adding and Reading 

Adding and Learning by Heart . 

Counting and Reading 

Counting and Learning by Heart 
Reading and Learning by Heart. 



1st 2nd 3rd 4th 5th 6th 7th 8th 



50 68 72 65 64 68 55 68 
58 67 70 75 81 71 54 58 
32 42 51 53 48 38 42 47 
10—02—03—03 03 02 25—08 
37 56 69 67 64 59 50 31 
01 14 24 18 05—18 22 26 
22 24—09—02—26 00—07—13 

—17—16—04 05 14—10—26—21 
24 —22 —27 —23 —15 —02 —16—21 

—05 07 08—10 19 05 03—10 



That increase or decrease would depend upon the kind of test 
and the stage of the subjects in the learning process, and be sub- 
ject further to such disturbing factors as fatigue, change in zeal, 
etc., seems quite evident. In concluding. Spearman and Krueger 
say that the lack of being accustomed to the test instead of act- 
ing as a cause of correlation, would act as a disturbing factor 



82 



Correlations of Mental Abilities 



lessening it. Which effect it would have, however, would surely 
vary according to circumstances. If conditions were such that 
the more intelligent could in the time allowed acquire a method 
that they could use to advantage, while the poorer ones did not 
get to that point, the correlations would be correspondingly high. 
If, on the other hand, conditions were such that even the best 
of the subjects were unable in the time allowed to hit upon 
and use effectively any intelligent method, their intelligence 
would count for little or nothing in determining the records, and 
the correlations would be correspondingly low or zero. 

Difference in quickness of adaptation is certainly in evidence 
in Binet's results, one illustration of which is given in the fol- 
lowing table: 





Number of 
Letters Marked 


Number op 
Errors 




Bright 


Dull 


Bright 


Dull 


1st period of 5 minutes 

2nd " "5 " 

3rd " "5 " 

4th " "5 " 

6th " "5 " 


115 

147 
176 
183 
213 


124 
12S 
179 
171 
207 


13.5 
10 

9 

3.5 

6 


43 
32 
15 

8 
7.5 



The improvement of the dull pupils in this cancellation test 
shows itself particularly with respect to the quality of the work. 
But difference in quickness of adaptation would seem a priori 
to be a characteristic applying to the learning of something of 
which both groups are capable, rather than to the factor of 
fundamental importance, differentiating the intelligent from the 
unintelligent. Of course a lower type of mind does adapt itself 
more slowly than a higher type of mind, but a more funda- 
mental difference between the inferior type of mind and the su- 
perior type, exists in the fact that there are certain kinds of 
performance to which the inferior mind is relatively incapable 
of adapting itself at all, such as the higher forms of abstraction. 
The tests here used by Binet are not such as to bring out this 
difference with any degree of clearness. They are largely along 
the line of perception and memory. The nearest approach to 
testing facility in the higher mental processes akin to abstrac- 
tion is in connection with the copying tests. The fact that there 



Comparison of Results With Those of Other Investigators 83 

is so decided a difference between the two groups with regard 
to the logical grouping of phrases in copying the easy and the 
difficult prose passages, suggests a difference which does not 
belong primarily under the category of quicker or slower 
adaptation. 

The method of this investigation and the tests used are sug- 
gestive, and worthy of leading to a more extended investigation 
along this line; and it would surely be worth while for some- 
one to take those of the tests found to be most satisfactory, 
and see what their reliability is with a larger number of subjects. 
Then if correlations between the different tests were calculated, 
more definiteness would be given to the work already begun. 
However, what we need most of all is the devising of tests of 
different forms of the highest mental processes — performances 
such that the duller minds cannot learn them so readily as they 
do feats of perception. 

In copying the easy material the bright pupils copied 4.5 
words at a time and the dull pupils 3.4; in copying the dif- 
ficult material the bright copied on the average 2.8 words and 
the dull 2.4. The grouping of phrases was far more logical with 
the bright than vv^ith the dull. On the other hand, in the copy- 
ing of nonsense material the dull pupils did fully as well as the 
bright. The difference here would seem to be one of appercep- 
tion:' When it came to copying nonsense material both groups 
were equally at a loss, as neither had at hand any means of or- 
ganizing the material. Doubtless continued practice at this 
would have revealed a quicker adaptation, and an earlier rise 
in the curve of learning in the case of the bright pupils than in 
the case of the dull, owing to their being quicker to find a 
method of organizing the new material. However, we could not 
hope to arrive at the true correlations of an ability with general 
intelligence if we took our individual records at a point in the 
learning curve where the dull group were still practically at 
zero efficiency, while the bright group had just made a sudden 
rise. Any such decided unevenness in the learning curve, un- 
less eliminated by averages, would seriously interfere with the 
securing of the true correlation between the characteristic 
ability of the group in that capacity, and general intelligence. 

Binet finds that in tactile sensibility the intelligent are de- 



84 Correlations of Mental Abilities 

cidedly superior in the first trials to the unintelligent. It is 
questionable here whether quickness in comprehending the in- 
structions was not a prominent factor in the results secured. 
When the dull can, in so small a number of practice trials, al- 
most equal the bright, who have meanwhile had an equal number 
of practice trials, it seems evident that the ultimate and real 
difference between the two groups in this capacity is not a large 
one. The difference with respect to speed of adaptation is a 
general factor that would tend to cover up or disguise the real 
correlations between different capacities themselves, and not aid 
materially in the detailed diagnosis of intelligence. It is sug- 
gestive, too, that in some of the tests the dull pupils did as well 
as the bright. May this not mean simply that the correlations 
between this sort of ability and general intelligence are too small 
to be brought out by such crude measurements and treatment of 
them as Binet employed? 

Hence to speak of the difference between inferior and su- 
perior minds as fundamentally a difference in power of volun- 
taiy attention, seems misleading in that it is too general a state- 
ment. It suggests that voluntary attention is a capacity that 
can be applied equally well in any desired direction, to the ex- 
tent of one's general ability. It errs in implying that there are 
not various kinds of voluntary attention, that do not correlate 
perfectly with one another. On the contrary, there are many 
varieties of voluntary attention — if we are to express the facts 
in Binet's terminology — for one might give a degree of atten- 
tion to music that he could by no means give to mathematics 
or to painting. Difference in quickness of adaptation there cer- 
tainly is, and this difference is one of no little significance ; but it 
is one of degree. A more significant difference between inferior 
and superior minds is one so pronounced as to suggest a dif- 
ference in kind, rather than one in degree merely. 

By this we mean that there are certain kinds of mental 
feats that can be performed by the able mind that can scarcely 
be performed by the inferior grade of mind at all, let its pos- 
sessor practice at it as much as he will. This sort of distinc- 
tion is not suggested by Binet's way of stating it — that the de- 
termining factor is a matter of voluntary attention. 



Comparison of Results With Those of Other Investigators 8 5 

Spearman and Krueger ('06) published the results of an in- 
vestigation on the correlations existing among the following 
mental abilities : Touch Discrimination, Tone Discrimination, 
Adding, Learning by Heart (a series of numbers), Ebbinghaus 
Mutilated Text. Their subjects were eleven advanced univer- 
sity students, four of whom did not speak German as their 
mother tongue. 

As to correlation between the two trials of the same test, 
Spearman and Krueger's coefficient for Adding is 76; ours are 
91 for the combined groups, 76 for the Good, and 90 for the 
Poor. This agreement is close. In the Ebbinghaus test their 
coefficient of reliability is 76 ; ours are 92, 96, and 90 — consider- 
ably higher doubtless on account of the greater number of trials 
and the method of scoring. In Sensory Discrimination their re- 
sults on Touch Discrimination and Tone Discrimination may be 
compared with ours on Drawing Lines. For Touch Discrimina- 
tion their coefficient is low, namely 42, For Tone Discrimina- 
tion their coefficient is 87, as compared with ours for drawing 
lines 72, 42, and 95. Their coefficient for Learning by Heart, 
92, is a good deal higher than ours for Unrelated Words, 73, 
48, 49; and somewhat higher than ours for Memory of Pas- 
sages, 90, 78, 83. 

It is well that our attention has been called to the fact that 
very different results may be obtained by two different experi- 
menters using the same tests. However, the fact. that there is 
such close correspondence as to reliability coefficients, where 
they are at all comparable, would go to show that when the test 
is itself satisfactory, and where the experimenter understands 
his business, there is no necessity that the investigations be con- 
ducted by two different experimenters. This precaution applies 
rather to the use of a new and untried test, not to one whose 
method of procedure is clearly understood, provided it is other- 
wise reliable as a test. Once the conscientious investigator is 
aware of the possibility of inaccuracy from such a source, he 
should be able, with our present knowledge of former errors 
in the conduct of mental tests, to secure by himself results that 
will not be vitiated by the personal equation. 



86 



Correlations of Mental Abilities 



The Pearson coefficients of correlation which they obtained 
among the abihties tested are as follows : 



Learn- 
ing by 
Heart 



Raw Coefficients: 

Adding 

Ebbinghaus test 

Tone Discrimination . . 
Touch Discrimination . 
Learning by Heart. . . . , 

Corrected Coefficients 

Adding 

Ebbinghaus test 

Tone Discrimination . . 
Touch Discrimination . 
Learning by Heart 





Ebbing- 


Tone 


Touch 


Adding 


haus 


Discrim- 


Discrim- 




test 


ination 


ination 




79 


67 


19 


79 




59 


00 


67 


59 




29 


19 


00 


29 




14 


—07 


17 


—13 




70 


68 


? 


70 




64 


? 


68 


64 




? 


? 


? 


? 




? 


? 


■ ? 


? 



14 
-07 

17 
-13 



Thus between Adding and Ebbinghaus test they get a correla- 
tion of 79 raw, and yo corrected; while ours are 71, 61, 65 
raw, and 71, 55, 63 corrected. It is interesting to note that with 
their results as with ours, the coefficient of correlation becomes 
lessened when corrected. One would expect their coefficient of 
correlation to correspond approximately with ours for the Good 
group. It may be, however, that their group represents persons 
of considerably greater variability than our good group, in 
which case the correlation would be higher. In one respect at 
least their results would be much less reliable than ours, namely, 
in the number of subjects tested. They used eleven subjects 
for the Adding test and only seven for the Ebbinghaus test, the 
foreigners being excluded. Then, too, it may be that as the sub- 
jects were not all of the same nationality, the correlation of 
Adding with other capacities may be largely influenced by dif- 
ferences of practice in adding, characteristics of the different 
countries represented. 

Spearman and Krueger did not give the corrected coefficients 
for Learning by Heart and the other four abilities tested. They 
put them down as zero because they are less than five times the 
P. E. Their raw coefficients are on the whole much lower than 



Comparison of Results With Those of Other Investigators 87 



the correlations we find between Memory of Words and Adding, 
Ebbinghaus test, and Discrimination of Lengths, as will be seen 
in the following: 

Raw Pearson Coefficients — According to Our Results 



Combined 


Goods 


49 


21 


94 


54 


21 


—01 


28 


19 



Poors 



Memory of Words and Adding 

" " " Ebbinghaus test . . . . 

" " " Drawing Lengths. . . 

" " Estimating Lengths 



22 
68 
Co 
04 



Spearman and Krueger conclude that there are beyond doubt 
positive and fairly high correlations between abilities as varied 
as Discrimination of Tones, Adding, and the Ebbinghaus test; 
and on the basis of Oehrn's data, between Speed of Reading, of 
Writing, and of Counting; and that the size of these different 
correlations is to be explained on the basis of the degree of 
their connection with a hypothetical, common central factor. 
They think there is good reason for believing that the central 
factor is not to be explained by individual differences in the 
zeal of the subjects, their momentary disposition, their being 
accustomed to the conditions of the experiments, their ability to 
make the most of help given, or to the power of their attention. 
They think that the explanation is in all probability psycho-phys- 
ical, consisting in the fact that one nervous system is more 
highly plastic than another, and that this would be the condition 
for the development of more precise and constantly functioning 
complexes of conduction, which would make possible greater 
quickness and accuracy. 

The suggestion that the explanation of differences in intelli- 
gence is psycho-ph3^sical, in itself explains nothing. Of course 
mental differences are determined by neural factors. Beyond 
this guarded general suggestion Spearman and Krueger scarcely 
seem to venture in the way of definite positive statement, except 
to state that the size of the different positive correlations is to 
be explained on the basis of the degree of connection with a 
hypothetical common central factor. 

Spearm.an ('04) reached conclusions that he considered veiy 



88 Correlations of Mental Abilities 

important for the measurement and diagnosis of general intelli- 
gence. " On the whole then we reach the profoundly impor- 
tant conclusion that there really exists a something which we 
may provisionally term General Sensory Discrimination, and 
similarly a General Intelligence, and further that the functional 
correspondence between these two is not appreciably less than 
absolute." Also, "... the common and essential element 
in the Intelligences wholly coincides with the common and es- 
sential element in the Sensory Functions." While these state- 
ments, taken in connection with the context, seem perfectly clear 
as to their meaning, it is evident that Spearman does not now 
hold to this latter statement as originally worded.^ 

That there is practically perfect correlation between Sensory 
Discrimination and General Intelligence certainly cannot be 
maintained. Dr. E. L. Thorndike ('09) investigated the rela- 
tionship between accuracy in Sensory Discrimination and Gen- 
eral Intelligence. He took two groups of subjects: (i) 37 
young women students in a normal school, (2) 25 boys in their 
third year in high school. For tests of Sensory Discrimination, 
Thorndike took 90 trials of each individual's accuracy in draw- 
ing lines to standards of 100, 75 and 50 mm., and 16 trials of 
each subject in weighting boxes to standards of 100 and 200 g. 
As a measure of General Intelligence, each girl was rated for 
general intelligence by all the rest, and also by 8 of the pro- 
fessors in the normal school. The scholastic records of the 
girls were also used. The boys were similarly rated by 6 of 
their fellows and by 4 professors. The tests were given on 
different days to eliminate common disturbing factors. The 
median deviation in age for girls was 10 months, and for the 
boys I year. 

The results are summed up in the form of Pearson coefficients 
of correlation (raw) as follows: 



^ On page 165 of Cyril Burt's article cited below, footnote 3, he says : 
"With reference to my criticism of the passage cited above (p. 159) 
formulating his view of the relation of General Sensory Discrimination 
and General Intelligence, Dr. Spearman has written me : ' This conclu- 
sion of mine was badly worded. I did not mean (as others have naturally 
taken it) that general intelligence was based on sensory discrimination; 
if anything, vice versa. I take both the sensory discrimination and the 
manifestations leading a teacher to impute general intelligence to be based 
on some deeper fundamental cause, as sketched in the Zeitschrift fiir 
Psychologie, Vol. XLI. p. no, par. 5.'" 



Comparison of Results With Those of Other Investigators 89 





Women 


Boys 


Discrimination of lengths, 1st half with 2nd half 

Discrimination of weights, 1st half with 2nd half 

Pupils' impressions of intellect, 1st half with 2nd half. . . . 
Teachers' impressions of intellect, 1st half with 2nd half. . 
Academic record, 1st half with 2nd half . 


66 
50 
91 
72 
62 


69 

72 

87 


Combined teachers' and pupils' impressions, 1st half with 
2nd half 


87 







Thus the measures of the two phases of Sensory Discrimina- 
tion and the estimates of General Intelligence were satisfactory 
as to reliability. The inter-correlations found were: 



Boys 



Scores for all lines with those for all weights 

Scores for all lines with pupils' impressions of intellect. . 

Scores for all lines with teachers' impressions of intellect . 

Scores for all lines with teachers' and pupils' impressions 
of intellect 

Scores for all lines with academic record 

Scores for all weights with pupils' impressions of intellect 

Scores for all weights with teachers' impressions of intellect 

Scores for all weights with teachers' and pupils' impres- 
sions of intellect 

Scores for all weights with academic record 

Pupils' impressions of intelligence with teachers' impres- 
sions 

Pupils' and teachers' impressions with academic record. . 

Combined weights and lines with pupils' and teachers' 
impressions 

Combined weights and lines with pupils' and teachers' 
impressions and academic record 



25 



05 
-01 



20 
21 



54 



14 



Hence the coefficient, corrected by the Spearman methods, be- 
tween 1st, factor common to accuracy in lines and weights, and 
factor common to pupils' and teachers' impressions of inte.lli- 
gence, is 20; 2nd, factor common to accuracy in lines and 
weights, and factor common to combined teachers' and pupils' 
im.pressions and academic record, is 25. According to this, the 
most probable correlation between General Sensory Discrimina- 
tion and General Intelligence would be about 23. 

Burt's results on this point (cited below) are difficult to in- 
terpret on account of the somewhat conflicting results in the 
different groups. If, however, we permitted ourselves to take 
the average of Burt's correlations between different forms of 



go Correlations of Mental Abilities 

Sensory Discrimination and Estimated Intelligence, we find it to 
be about 21. 

There still remains Spearman's provisional theory of a 
hierarchy of mental functions as the explanation of the fact of 
general intelligence. " Wherever branches of intellectual ac- 
tivity are at all dissimilar, then their correlations with one 
another appear wholly due to their being all variously saturated 
with some common fundamental Function (or group of Func- 
tions)." " . . . the remaining or specific elements of the 
activity seem in every case to be wholly different from that in 
all i\\t others." 

According to this theory, no two mental functions could be 
more closely related to one another than each is related to the 
common central factor. For instance in our results, Memory 
of Words and Memory of Passages should relate no more 
closely to each other, and the A test and Geometrical Forms no 
more closely to each other, than the element common to Memory 
of Words and Memory of Passages relate to the element 
common to the A test and Geometrical Forms. This can be 
very readily tested by the use of the correction formula, 

Rp^q^ + Rp,q, + Rp.Ax + Rp'^(l2 
Rpq = 4 , where Rpq represents 

^Rp,p, X Rq,q, 
the correlation between the common factor in p-^^ and p.2, and the 
common factor in q-^ and g,/ ^PiQi represents the correlation be- 
tween the ability tested by, say, Memory of Words and the 
ability tested by the A test; i^/'i^a represents the correlation be- 
tween the ability tested by the Memory of Words test and the 
ability tested by the Geometrical Forms test; i^/'o^i represents 
the correlation between the abilities tested by Memory of Pas- 
sages and the A test; and Rp^qo represents the correlation be- 
tween the abilities tested by Memory of Passages and the 
Geometrical Forms test. 

Then taking the estimated true coefficients of correlation 
from Table XIV, and substituting the values in the above equa- 

54 + 49 + 4<3 + 33 
tion we get, Rpq rr= 4 = 54. 

V80 X 87 
which is much lower than Rpipo, 80, or Rq-^q<,, 87. 



Comparison of Results With Those of Other Investigators g i 

That is, Memory of Words and Memory of Passages are more 
closely related one to another, and A test and Geometrical Forms 
are more closely related one to another than the factor common 
to the first two is to the factor common to the second two. 

Similarly facts for the abilities tested by the Ebbinghaus and 
Hard Opposites tests, and the A and Geometrical Forms tests, 
letting P1P2Q1 and q^ refer to these in order, are that 

54 + 36 + 58 + 42 
Rpq= 4 =55, which is much below 85 or 87. 

V85 X 87 

Again on the basis of Spearman's theory of a common central 
factor, if the coefficients of correlation among a number of abili- 
ties are arranged in descending order, from left to right and 
from top to bottom as are the ones he obtained on page 86 
above, in every line the figures should be in descending order as 
they are on the top line and on the vertical line on the left. 
According to our results, secured from 37 subjects instead of 
only II, this is by no means the case, as is evident from the fol- 
lowing from Table XIV, p. 63. 









00 












CO 

s 








Tj 




c3 












OQ 

'm 


U 





CO 

c3 

Ph 




■3 









3 





tH-C 





t+-t 




Ph 




rt 




§ 


£< 





Oh 















^ 
y 


^ 


b 


n 


t? 


bC 


be 
a 




H 




C 

3 


-s 




a 


>> 




a 


.2 


a 


to 


a 




-Q 




(V 


o3 


<o 


TJ 






ID 




w 


W 


^ 


W 


§ 


< 


^ 


< 


a 


Ebbinghaus test 


85 


85 


82 
84 


72 
88 


71 
70 


65 
70 


60 

56 


54 

58 


36 


Hard Opposites 


4?, 


Memory of Words 


8? 


84 




65 


80 


39 


65 


54 


49 


Easy Opposites 


l'^, 


83 


65 




50 


56 


37 


50 


45 


Memory of Passages 


71 


70 


80 


50 




42 


30 


46 


33 


Adding 


65 


70 


3q 


56 


49 




39 


58 


30 


Learning Pairs 


60 
54 
36 


56 
58 
42 


65 
54 
49 


30 
50 
45 


39 
46 
33 


39 

58 
30 


36 
36 


36 

87 


36 


A test 


87 


Geometrical Forms 









Thus it is quite evident that Spearman's theory is not in har- 
mony with the facts we have secured. 

Cyril Burt ('09) tested 43 boys between the ages of 12 years 



92 



Correlations of Mental Abilities 



6 months and 13 years 6 months, one group of 13 boys from a 
high class College Preparatory School, and the remaining group 
of 30 from an Elementary School. The tests used can be 
grouped as follows : 

I. Sensory Discrimination. 

Touch, weights, pitch, lengths. 
II. Motor Tests. (Simple reactions). 
Tapping, card dealing. 

III. Sensory Motor Tests. 

Card sorting, alphabet finding. 

IV. Association Tests. 

Immediate memory — concrete words, abstract words, 

nonsense syllables 
Mirror test — formation of motor association by trial 

and error. 
Spot pattern test — apperception of a form composed 
of dots. 
V. Test of Voluntary Attention. 
Dotting irregular dots. 

The correlations found by Burt are as follows : 



Corrected Coefficients 
for 

Elementary School 



Imputed Intelligence . 

Spot Pattern 

Dotting 

Mirror Tracing 

Alphabet 

Tapping 

Memory 

Dealing 

Sorting 

Somid 

Lines 

Touch 

Weight 






1 
























'-^ 






bf) 

























^ 


















f-* 






















a, 




TJl 


.S 

"0 
Q 


U 

P 




'a, 
< 


bC 

"a 




S 


bJD 



bJD 






3 







100 


75 


74 


68 


65 


60 


54 


53 


52 


51 


17 


100 




80 


75 


96 


64 


41 


66 


68 


55 


50 


21 


75 


80 




84 


85 


83 


22 


83 


75 


68 


60 


30 


74 


75 


84 




71 


48 


13 


72 


64 


40 


16 


27 


68 


96 


85 


71 




67 


47 


83 


83 


68 


37 


66 


65 


64 


83 


48 


67 




01 


79 


78 


53 


16 


12 


60 


41 


22 


13 


47 


01 




18 


27 


19 


05 


15 


54 


66 


83 


72 


83 


79 


18 




77 


41 


59 


32 


53 


68 


75 


64 


83 


78 


27 


77 




25 


32 


20 


52 


55 


68 


40 


68 


53 


19 


41 


25 




-05 


-01 


51 


50 


60 


16 


37 


16 


05 


59 


32 


-05 




26 


17 


21 


30 


27 


66 


12 


15 


32 


30 


-01 


26 




-01 


27 


07 


-10 


26 


11 


07 


05 


23 


06 


-16 


37 



01 
27 
07 
-10 
26 
11 
07 
05 
23 
06 
-16 
37 



Comparison of Results With Those of Other Investigators 93 



Corrected Coefficients 

for 

Preparatory School 



Sorting 

Dotting 

Alphabet 

Tapping 

Imputed Intelligence 

Memory 

Mirror 

Spot Pattern 

Dealing 

Lines 

Touch 

Weight 

Soimd 





t>0 

a 



Q 


-1-2 

-a 
< 


a 
"a 




a 

,bC 

1— 1 




s 


It 
S 


s 

P-( 

&, 
02 


be 


1 
i5 




3 


Eh 


1 




100 


100 


100 


100 


90 


71 


47 


32 


07 


-32 


-33 


100 




84 


73 


96 


84 


100 


62 


-17 


45 


31 


25 


100 


84 




94 


91 


100 


56 


83 


37 


32 


-48 


-06 


100 


73 


94 




41 


80 


100 


50 


36 


57 


09 


74 


100 


96 


91 


41 




82 


68 


66 


06 


44 


-17 


-20 


90 


84 


100 


80 


82 




64 


84 


06 


27 


27 


22 


71 


100 


56 


100 


68 


64 




75 


-61 


94 


40 


71 


47 


62 


83 


50 


66 


84 


75 




40 


85 


-29 


10 


32 


-17 


37 


36 


06 


06 


-61 


40 




-07 


-51 


-40 


07 


45 


32 


57 


44 


27 


94 


85 


-07 




21 


15 


-32 


31 


-48 


09 


-17 


27 


40 


-29 


-51 


21 




61 


-33 


25 


-06 


74 


-20 


22 


71 


10 


-40 


15 


61 




-62 


63 


35 


44 


41 


27 


93 


40 


-06 


23 


26 


53 



62 
63 
35 
44 
41 
27 
93 
40 
-06 
23 
26 
53 



The above are arranged approximately in descending order, 
but it is very evident that they even more strongly contradict 
Spearman's original theory of a hierarchial arrangement than 
do our results spoken of above. Apparently, however, Spear- 
man himself has abandoned or modified this view. In his 
demonstration of a " Hierarchy of Coefficients," Burt uses the 
raw coefficients from the amalgamated measurements, rather 
than the corrected coefficients which we have quoted. In this 
connection he says : " Dr. Spearman and Prof. Krueger imply 
that satisfactory hierarchies are exhibited only by the ' pure ' or 
theoretical coefficients ; but it appears that those based on amal- 
gamated measurements are better than those based on theoreti- 
cal ' correction,' if the experimental conditions are carefully con- 
trolled." ..." The theoretical values for the ideal hier- 
archy may be obtained by various mathematical formulae." 
" The following simple formula has been supplied for this pur- 
pose by Dr. Spearman (to whom I am here particularly in- 
debted for several improvements on my own demonstration of a 
hierarchy). . . ." But when the raw coefficients fail to ac- 
cord with the theory, and when the corrected coefficients fail to 
accord with the theory, and when coefficients from amalgamated 



94 Correlations of Mental Abilities 

series of measurements fail to accord with the theory, why not 
abandon the theory! Surely this would be better than to re- 
sort to further manipulation of data influenced to some extent 
by variables at present uncertain, and consequently to that extent 
untrustworthy. Only when the variables themselves are fully 
and definitely understood can such methods be used with any 
degree of safety. 

Burt does not give the correlations between memory of con- 
crete words, memory of abstract words, and memory of non- 
sense syllables. In comparing his results with ours we shall 
take his data for the boys of the Elementary School, both be- 
cause the greater number of subjects in this group makes the 
results more reliable than in the case of the other group, and 
because the group itself is probably more representative of 
average boys than are boys in a College Preparatory School. 
Perhaps the fairest comparison to make would be between his 
coefficients for the Elementary School Group, and our estimated 
true coefficients, though one would expect the latter to be some- 
what higher. 

Burt's corrected coefficient for Memory and the Spot Pat- 
tern test is 41 ; between Memory of Words and Learning Pairs, 
we get for the Poor group 44, and for the estimated true co- 
efficient 65. The agreement here is as close as could be ex- 
pected. 

As to correlation between Sensory Discrimination and 
Memory, Burt gets a correlation between Discrimination of 
Lines and Memory of 05 ; between Drawing Lengths and 
Memory of Words we get -09 for the Poor group, and -05 as 
the estimated true correlation. 

Bonser ('10) gave tests in reasoning and selective thinking 
to 385 boys and 372 girls of the Fourth, Fifth and Sixth school 
grades of public schools in Passaic, New Jersey. " The tests 
employed were made up of a series of problems and questions 
designed to exercise the most fundamental four phases of 
reasoning activity, namely : The mathematical judgment ; con- 
trolled association ; selective judgment ; and that complex of 
analytic and synthetic thinking used in the intellectual interpre- 
tation of literature. 



Comparison of Results With Those of Other Investigators 95 

Mathematical Judgment 

" The problems for testing the mathematical judgment were of 
two kinds, two sets of five each, I, A and B, stated in the form 
usually followed in current text-books in arithmetic; and two 
sets of five each, II, A and B, of the same difficulty as the pre- 
ceding in processes involved but stated in a less conventional 
way. Each of the ten problems of the first type may be called 
a " two-step " problem — it requires a preliminary operation for 
securing the intermediate datum necessary before the final 
operation can be accomplished. 

Tests I and II 

" I. A. Get the answers to these problems as quickly as you 
can. 

1. If 54 of a gallon of oil costs 9 cents, what will 7 gallons cost? 

2. John sold 4 sheep for $5 each. He kept J^ of the money and with 

the other '^4 he bought lambs at $2 each. How many did he buy? 

3. A pint of water weighs a pound. What does a gallon weigh? 

4. At I2l4 cents each, how much more will six tablets cost than 10 

pens at 5 cents each? 
5 At IS cents a yard, how much will 7 feet of cloth cost? 

B. 

A man whose salary was $20 a week spends $14 a week. In how 

many weeks can he save $300? 
How many pencils can you buy for 50 cents at the rate of 2 for 5 

cents ? 
A man bought land for $100. He sold it for $120, gaining $5 an 

acre. How many acres were there? 
A man spent j4 of his money and had $8 left. How much had he at 

first? 
The uniforms for a baseball nine cost $2.50 each. The shoes cost $2 

a pair. What was the total cost of uniforms and shoes for the 

nine? 

II. A. 

I. 132 plus what number equals 36? 

2 If John had 15 cents more than he spent today he would have 40 
cents. How much did he spend today? 

3. What number minus 7 equals 23? 

4. If James had 4 times as much money as George, he would have $16. 

How much money has George? 

5. What number added to 16 gives a number 4 less than 27? 



96 Correlations of Mental Abilities 

B. 

1. What number subtracted 12 times from 30 will leave a remainder 

of 6? 

2. If a train travels half a mile a minute, what is the rate per hour? 

3. What number minus 16 equals 20? 

4. What number doubled equals 2 times 3 ? 

5. If 7 multiplied by some number equals 63, what is the number? 

" In the original blanks, immediately following each problem 
space was left for its solution. 

Controlled Association 

" For controlled association, three types of tests were used. 
First, two sets of ten sentences each, III, A, a and b, were given 
with a significant word omitted from each to be filled in by the 
pupil. Second, two sets of ten sentences each, III, B, a and b, 
were given in each of which two significant words were placed, 
one above the other, one giving a correct meaning to the sen- 
tence, the other an erroneous meaning, the pupil to draw a line 
through the wrong word leaving the sentence so that it would 
read correctly. Third, three sets of twenty words each, IV, A, 
B and C, were given to pupils, they to write beside each respec- 
tive word a word just its opposite in meaning — the familiar 
" opposites " test. 

Tests III and IV 

" III. A. a. Complete the following sentences as quickly as 
you can by filling the blank spaces with appropriate words : 
I always comes in the last week in December. 

2. A is one who plays a musical instrument. 

3. The city is in Russia. 

4 are large, visible bodies of watery vapor floating about 

in the air. 

5 used for building houses are made of clay. 

6. The machine on a railroad for drawing cars is an 

7 is the most useful metal for blacksmiths. 

8 live and swim about in the water. 

9. Most light summer clothing is made of goods. 

10 is a holiday. 

III. A. b. 

1. The flesh of cattle used for food is called 

2. The months are June, July and August. 

3. The makes it light during the day. 



Comparison of Results With Those of Other Investigators 97 
catch many mice and birds. 



A is a large stream of water flowing through the land. 

Men who live in the country and till the soil are called 

is a mineral which we burn. 

The Ocean is east of the United States. 

sell sugar, vegetables and other foods. 

There are hours in half a day. 



III. B. a. As quickly as you can, make these sentences cor- 
rect by drawing a line through the wrong word where two words 
occur, one above the other : 

longer * 

1. Days are in summer than in winter. 

shorter 

up 

2. Water always flows hill. 

down 

more 

3. Glass breaks easily than tin. 

less 
earlier 

4. The sun rises in January than in July. 

later 
softer 

5. Iron is than wood. 

harder 
warmer 

6. It is in Florida than in Maine. 

colder 

heavier 

7. Anything that floats is than water. 

lighter 
more 

8. Oranges grow satisfactorily in California than in New Jersey. 

less 
shorter 

9. Shadows are in summer than in winter. 

longer 
more 
10. Plants grow readily in warm sunshine than in the cool shade, 

less 

III. B. b. 

stronger 

1. Men are usually than women. 

weaker 

less 

2. A pound of iron is worth than a pound of copper. 

more 
before 

3. Christmas comes Thanksgiving day. 

after 



98 



Correlations of Mental Abilities 



warmer 

4. Cotton clothing is than wool. 

cooler 
Less 

5. coal is used in summer than in winter. 
More 

poorer 

6. Bankers are than cab drivers. 

richer 
More 

7. horses than mules are used for driving purposes. 
Fewer 

more 

8. There are teachers than preachers. 

fewer 

more 

9. Oranges are sweet than lemons. 

less 
More 
10. bread than cake is eaten in this city. 

Less 

IV. As quickly as you can write beside each of these words 
a word that means exactly its opposite. 



A. 


B. 


C. 


day- 


great 


bad 


asleep 


hot 


inside 


absent 


dirty 


slow 


brother 


heavy 


short 


best 


late 


little 


above 


first 


soft 


big 


left 


black 


backwards 


morning 


dark 


buy 


much 


sad 


come 


near 


true 


cheap 


north 


dislike 


broad 


open 


poor 


dead 


round 


well 


land 


sharp 


sorrj' 


country 


east 


thick 


tall 


known 


full 


son 


something 


peace 


here 


stay 


few 


less 


push 


below- 


mine 


nowhere 


enemy 



Selective Judgment 

" Two types of tests were used for selective judgment. First, 

two sel^, V, A and B, of two series each of ten reasons why 

some given fact is true, some of which reasons are correct, the 

others incorrect or irrelevant, were given. The pupil was to 



Comparison of Results With Those of Other Investigators 99 

select, by checking, the correct reasons. Second, there were 
given similarly two sets, IV, A and B, of three series each, of 
five definitions for a given thing or term, some of which were 
correct, the others incorrect or irrelevant: 



Tests V and VI 

" V. A. The following reasons have been given to show why 
New York has become a larger city than Boston, As quickly 
as you can, place a cross like this, +, before each reason you 
think a good one: 

New York is on an island. 

More foreigners live in New York than in Boston. 

3. New York is on a large river coming from a rich agricultural region. 

4. Mr. Rockefeller has a fine home in New York. 

5. New York has more churches than Boston. 

6. New York has better communication with the States lying to the 
west. 

New York has elevated railroads. 

New York is in the midst of a rich fruit and agricultural district. 
9. New York is nine or ten years older than Boston. 
10. New York has a republican governor. 

B. These reasons have been given to show that oak is better 
than pine for making furniture. Check the good reasons. 

1. Oak wood is harder than pine. 

2. Oak trees have acorns, pine trees do not. 

3. Oak wood takes a finer polish than pine. 

4. Oak trees have more beautiful leaves. 

5. Oak trees make good homes for squirrels. 

6. Pine wood will not last so long as oak. 

7. Pine is more easily dented and defaced than oak. 

8. When polished and varnished, oak is much more beautiful than pine. 

9. Pine trees are sometimes used for Christmas trees. 
10. Oak trees are easier to climb than pine trees. 

C. The following reasons have been given to show why 
oranges grow better in Florida than in New Jersey. Check the 
good reasons. 



There are many negroes in Florida who work very cheaply. 
Florida has warm summer weather almost the whole year. 
There are no alligators in New Jersey. 
Florida very rarely has hard frosts. 
New Jersey is not so large as Florida. 
Florida was settled earlier than New Jersey. 
New Jersey grows many fine peaches. 
Florida has a very moist, warm climate. 



lOO Correlations of Mental Abilities 

g. Florida is a word meaning the land of flowers. 
ID. Florida is a popular winter resort. 

D. Among these reasons why horses are better than cattle 
for driving and working animals, check those which you think 
are good reasons. 

1. Horses are more intelligent than cattle. 

2. Cattle are not so tall as horses. 

3. Horses like corn, oats and hay. 

4. Horses are much more active and walk faster than cattle. 

5. Cattle are extensively used for food. 

6. Horses are much more beautiful and graceful than cattle. 

7. The skins of horses are sometimes made into gloves. 

8. Horses are more easily trained and controlled than cattle. 

9. President Roosevelt likes to ride on horseback. 

10. Horses have more rapid and varied gaits than cattle. 

VI. A. In the following definitions, place a small cross, like 
this +, before those which you think are good ones, doing it as 
quickly as you can. 

a. Definitions of a shoe. 

1. A portion of clothing. 

2. Something black made of leather. 

3. A protective covering for the feet, usually made of leather, 

having a firm bottom or sole and flexible upper portions, an 
opening for the foot being fastened by lacings, buttons or 
buckles. 

4. Something to wear on the feet. 

5. A necessary article costing from one to five or six dollars. 

b. Definitions of an island. 

1. A piece of land out in the water. 

2. A small body of land. 

3. A body of land entirely surrounded by water. 

4. Cuba is an island. 

5. A portion of land rising above the surrounding level. 

c. Definitions of to explode. 

1. To burst suddenly with a loud noise. 

2. To knock all to pieces. 

3. To make a very loud noise. 

4. To fill the air with a tumultuous roar. 

5. To blow up. 

a. Definitions of a chair. 

1. A piece of household furniture. 

2. A movable seat with a back intended for one person. 

3. A piece of furniture on which to sit. 

4. Rocking chairs are comfortable chairs. 

5. A single seat having a back. 



Comparison of Results With Those of Other Investigators loi 

b. Definitions of to write. 

1. To make marks with a pen or pencil. 

2. To make characters which stand for ideas. 

3. To use a pen or pencil. 

4. To make marks on any kind of surface with any kind of an 

instrument which will express one's ideas so that another 
may understand them. 

5. To write a letter. 

c. Definitions of a buggy. 

1. A buggy is black. 

2. A buggy is something to ride in. 

3. A buggy is a light, four wheeled vehicle, with or without a 

top or covering, designed for carrying two or three persons. 

4. A buggy is drawn by horses. 

5. A buggy may have rubber tires. 

Literary Interpretation 

" For literary interpretation, two stanzas of poetry, VII, A and 
B, were used, the pupil to write the meaning of each in his own 
words. These poems are taken from a third reader and a 
second reader respectively, each from a different standard series 
published within a decade of the time of these tests. 

Test VII 

" VII. A. Read carefully the following stanza, then write its 
meaning in your own words. 

' This little rill, that from the springs 
Of yonder grove its current brings, 
Plays on the slope awhile, and then 
Goes prattling into groves again, 
Oft to its warbling waters drew 
My little feet, when life was new.' 

B. Read carefully the following stanza, then write its mean- 
ing in your own words : 

' Under the greenwood tree, 
Who loves to lie with me. 
And tune his merry note 
Unto the sweet bird's throat, 
Come hither, come hither, come hither, 

Here shall he see 

No enemy 
But winter and rough weather.' 



I02 Correlations of Mental Abilities 

Spelling 

" As an incidental problem for correlation, the opportunity 
offered for a test in spelling was taken. Two papers, B and C, 
from test V, the opposites test, were graded in spelling for each 
pupil. As the pupils did not know that the papers were to be 
graded in spelling, it had little of the disadvantages of the 
formal spelling test, yet the words were practically predeter- 
mined and uniform." 

Bonser's results are given in part in the following table: 



TABLE XX 

Averages of Coefficients of Correlation by 
AND for Both Grade and Age 


Grade, by Age, 




Boys, 385 


Girls 


,372 


Total, 757 




By 

Grade 


Age 


By 

Grade 


By 

Age 


By Grade 

and Age 


I-II and III 


■ 39 
33 
21 
10 
18 
38 
16 

55 

38 
25 
40 

■ 62 
27 

41 
35 

26 
87 
04 

45 
22 
70 
07 

23 
60 
03 

32 

27 

02 


58 
49 
44 
38 
48 
69 
34 

57 
45 
31 
48 
61 
35 

65 
45 
37 

87 
29 

54 

40 
79 
18 

28- 

63 

18 

49 
25 

30 


32 
31 
17 
31 
08 
58 
20 

54 
35 

21 
43 
58 
21 

34 
30 
28 
81 
25 

36 
09 
62 
06 

11 

59 
04 

27 
17 

23 


34 
53 
52 
25 
32 
70 
25 

47 
35 
16 
39 
40 
07 

56 
25 
35 

85 
28 

53 

34 
SO 
29 

32 
50 
13 

39 
30 

32 


41 


" "IV 


42 


" " V 


33 


"VI 


26 


« " VII 


26 


" " Total 


59 


" " Spelling 

Ill and IV 


24 
53 


« " V 


38 


" " VI 


24 


" " VII 

" " Total 


45 
55 


" " Spelling 

IV and V 


22 
49 


"VI 


34 


" VII 


32 


" " Total 


85 


" " Spelling 

V and VI 


21 

47 


" " VII 


26 


" Total 


73 


" " Spelling 

VI and VII 


12 

24 


" " Total 


58 


" " Spelling 

VII and Total 


09 

37 


" " Spelling 

Total and Spelling 


25 
22 



Comparison of Results With Those of Other Investigators 103 

Bonser concludes that the tests " are valid measures of sev- 
eral phases of that complex capacity we call reasoning ability. 
Group correlations are so much higher among these tests than 
among those so far produced among mental abilities more varied 
in kind that we are clearly justified in holding them to be tests 
of abilities which are varieties of one general species of 
ability." 

Bonser's coefficients of correlation are all obtained by the 
method of like and unlike signs, and are uncorrected for at- 
tenuation. " The highest coefficients as shown by the averages, 
are, in their order, that for tests III and IV, the two forms of 
controlled association, — completing sentences and opposites — 
53 ; that for tests IV and V, the opposites and the selection of 
reasons in one of the tests in selective judgment, 49; that for 
V and VI, the two tests in selective thinking, 47; and that for 
III and VII, controlled association and interpretation of poems, 
45. By correction these would all be raised to above 75, those 
for III and each of the others approaching 100 very closely." 
This last statement is made on the ground of a few coefficients 
of correlation that have been corrected by two different methods, 
and it must be remembered of course that this is only a rough 
estimate. However, the general fact that the correlations of the 
different tests of selective thinking with one another are rela- 
tively very high, is in accord with our results as shown in Tables 
IX, X, and XIV. 

Bonser further concludes that " the results here derived point 
to the conclusion that the correlations among the abilities here 
tested are a matter of native capacity rather than the result of 
training." This follows mainly from the facts that, (i) the cor- 
relations on the basis of age are considerably higher than those 
on the basis of grades ; (2) from the fact that the median age of 
the best 10 per cent and of the poorest 10 per cent is nearly the 
same, while in the scores obtained in the tests, they differ from 
three hundred to three thousand per cent. Moreover the chil- 
dren had had almost no training in the exact type of problems 
as set, in the opposites test, and in the form of selective judg- 
ment of test V, yet these stand, in this order, in the highest cor- 
relation to the total ability shown for all of the tests — all of 
which suggests that these abilities have not been developed as 



I04 Correlations of Mental Abilities 

by-products of school training, but that the results of the tests 
are measures of the native capacity of the children for the ac- 
tivities required in these problems. 

There is however a disturbing factor entering into Bonser's 
results which is worthy of consideration. It arises from the 
fact that in all tests except that of Opposites, the time element 
was not kept constant for all. All of the pupils were stopped at 
the moment when the first pupil of the room had just finished. 
Bonser does not state the time record in the different rooms, 
nor take it into consideration in scoring the results. Presum- 
ably the pupils in the higher grades would thus get less time 
for the work than those in the lower grades, in so far as the 
time taken by the quickest pupil in an upper grade would be 
less than the time taken by the quickest pupil in a lower grade. 
It would thus appear that Bonser's results underemphasize the 
superiority of the upper grades over the lower ones. It would 
tend to favor the younger pupils. While it would not affect the 
size of the correlations by grades, it would probably tend to 
raise somewhat, — and certainly to disturb more or less, — the 
correlations by age. How much this disturbance would amount 
to is difficult to say. It would probably be slight. Even grant- 
ing that it would be considerable, however, Bonser's contention 
that the tests measure native capacity rather than training, 
would still have sufficient to support it in the other arguments 
used, apart from that of the higher correlations by age than by 
grades. This conclusion also is in accord with our results. 

William Brown ('ii) records the results of a somewhat ex- 
tensive investigation " for the purpose of determining to what 
extent correlation exists between certain very simple mental 
abilities in cases where the individuals experimented upon are, 
as near as may be, identically situated with respect to previous 
practice, general training, and environment; and how closely, if 
at all, these elementary abilities are related to general intellec- 
tual ability as measured by teachers' judgments, school marks, 
etc. Every effort was made to keep the groups of individuals 
tested as homogeneous as possible; and instead of measuring 
irrelevant factors and ' correcting ' for them in the later stages 
of the research, the influence of such irrelevant factors was ex- 



Comparison of Results With Those of Other Investigators 105 

eluded right from the beginning by a rigorous segregation of 
the material, and in other ways. 

" The groups of individuals to which the tests were applied, 
were as follows : 

Group I, 66 boys of a London elementary school, all between 
the ages of 11 and 12. 

Group II, 39 girls oi a London elementary school, all between 
the ages of 11 and 12. 

Group III, 40 boys of a London higher grade school, all be- 
tween the ages of 11 and 12. 

Group IV, 56 training college students (women), of the same 
year and of approximately the same age. 

Group Va, 35 university students (men). 

Group Vb, 23 university students (women)." 

The tests employed were selected " not so much for their 
a priori likelihood of showing inter-correlation, as for their con- 
venience in admitting of application to an entire group of sub- 
jects simultaneously and unobtrusively. The following is a list 
of them: 

1. Crossing through letters e and r in a page of print. 

2. Crossing through letters a, n, o, and s in a page of print. 

3. Crossing through every letter in a page of print. 

4. Adding up single digits in groups of ten. Measurement 
of (a) speed, (b) accuracy. 

5. Bisecting ten printed lines (80 mm. long), and putting in 
one of the points of trisection in each of the ten other lines 
(90 mm. long). 

6. Muller-Lyer Illusion. Measurement of (a) size, (b) 
mean variation. 

7. Vertical-Horizontal Illusion. Measurement of (a) size, 
(b) mean variation. 

8. Mechanical Memory (permanent), tested by means of 
nonsense syllables. 

9. Memory for poetry. 

10. Combination test (Ebbinghaus mutilated test). 

In the case of groups I and II, recourse was also had to : 

11. Marks for Drawing. 

12. Total school marks. 



io6 Correlations of Mental Abilities 

13. Grading for General Intelligence (two independent 
measures). 

Finally with Groups Va, and Vb, the following test was also 
employed : 

14. Association-time (uncontrolled). Measurement of rate 
of sequence of ideas called up by a stimulus-word." 

The author does not seem to appreciate fully the inaccuracies 
which may creep in and influence the results, when the tests are 
given as group tests rather than to each individual separately. 

With the exception of test (9), and in some cases test (8), 
every test was applied twice, the second test being given about 
a fortnight after the first, and at the same hour of the day. 

It is highly probable that the gain in accuracy owing to the 
comparatively large number of subjects in the different groups 
is more than counterbalanced by the tendency to spurious cor- 
relation due to the tests being given as group tests, and by the 
inaccuracies due to the small number of measurements taken. 
However there is still need of considerable diversity of general 
method in investigations in correlation, to insure adequate cor- 
roboration and verification of results. 

Brown's numerical results are summarized in part in the fol- 
lowing tables : 



Comparison of Results With Those of Other Investigators 107 



Brown's Results. Pearson Coefficients op Correlation 
(Top line, Group I; 2nd line, Group II; 3rd line. Group III) 



- 






CO 





^ 
t 


^ 


1 


CO 
ID 






8 

a 

bC 




CI 


60 






'5 


^ 
"S 
b 







< 




e 

^ 
s 


c 



CO 


a 

I— * 




M 
" 


M 





43 




s 


+i 


-ij 


(1 






R 










^ 





T3 


t3 


-k^ 






a 




o3 


c3 




(D 


<0 


< 


^ 





s 




03 








78 


45 


40 


27 


59 


30 


53 


00 






Marking er 




80 


-15 


on 




13 


00 


49 




00 


00 






74 


00 


00 


23 


35 


00 


25 




30 


28 




78 




48 


29 


28 


51 


24 


21 


00 






Marking anas 


80 




00 


20 




00 


00 


21 




27 


13 




74 




10 


00 


14 


20 


-11 


00 




17 


10 




45 


48 




52 


52 


40 


38 


13 


15 






Ebbinghaus test .... 


-15 


00 




37 




-13 


-25 


00 




54 


43 




00 


10 




28 


44 


32 


00 


28 




60 


69 




40 


29 


52 




49 


27 


31 


14 


10 






Mechanical Memory. 


00 


20 


37 






-13 


-23 


00 




59 


55 




00 


00 


28 




38 


00 


00 


00 




40 


49 




27 


28 


52 


49 




41 


38 


12 


13 






Memory of Poetry.. 


























23 


14 


44 


38 




00 


-11 


19 




60 


57 




59 


51 


40 


27 


41 




13 


25 


00 






Addition (Speed).. . . 


13 


00 


-13 


-13 






24 


33 




00 


10 




35 


20 


32 


00 


00 




33 


20 




28 


24 




30 


24 


38 


31 


38 


13 




00 


41 






Addition (Accuracy) 


00 


00 


-25 


-23 




24 




30 




00 


00 




00 


-11 


00 


00 


-11 


33 




00 




11 


00 




53 


21 


13 


14 


12 


25 


00 




00 






Motor (all letters).. . 


49 


21 


00 


00 




33 


30 






00 


13 




25 


00 


28 


00 


19 


20 


00 






23 


32 




00 


00 


15 


10 


13 


00 


41 


00 








Bisection 
























School Marks 


00 


27 


54 


59 




00 


00 


00 






64 




30 


17 


60 


40 


60 


28 


11 


23 






78 


General Intelligence. 


00 


13 


43 


55 




10 


00 


13 




64 






28 


10 


69 


49 


57 


24 


00 


32 




78 





io8 Correlations of Mental Abilities 

Brown's Results. Pearson Coefficients of Correlation 
(Top line, Group IV; 2nd line, Group Va) 







^ 




b 










c3 


^,— ^ 


o 




0) 




1 


o 
o 




s 




s 






< 


^ 


"rt 




o 




,a 


fl 


d 




taO 


-u 




bC 


■-i3 




c3 








Xi 


T3 


X) 


o 


tH 






X! 


'TS 


73 


(B 


d 






H 


-3l 


<^ 


S 


S 


<1 


Ebbinghaus test 




53 


34 


31 










-16 


19 




19 


33 


Addition (accuracy) 


53 




43 


20 








-16 




38 




-26 


39 


Addition (speed) 


34 


43 




18 








19 


38 






00 


37 


Mechanical Memory 


31 


20 


18 












Marking er 
















19 


- 26 


00 






18 


Association time 


33 


39 


37 




-18 









The principal conclusions summed up by Brown are : " The 
correlation between different psychical abilities is not very close. 
Few correlations are greater than .60. 

" The size of the correlation coefficient varies greatly from 
one group of subjects to another. This shows how great is the 
danger of spurious correlation, due to heterogeneity of material, 
in psychical measurements. 

" The Combinations-Method of Ebbinghaus is a good measure 
of intellectual ability. It correlates with general intelligence 
almost as closely as scholastic intelligence (school marks) does. 
Mechanical memory correlates fairly closely with intelligence. 
Correlations may be very low even within a set of 
mental tests which appear to measure closely related mental 
abilities, and this when the reliability coefficients are high. Thus 
the correlation between erasing the letters a, n, o, s, and erasing 
all the letters, is less than three times the probable error in every 
group tested. 

" In homogeneous groups of subjects there is no positive evi- 



Conclusion 109 

dence of the existence of one ' central factor ' to which the cor- 
relations between the individual mental abilities may be regarded 
as due." 

Conclusions 
A — As to method: 

In general we have found it highly instructive to calculate 
correlations with two contrasting, selected groups, and also with 
the groups combined. The correlations obtained in one group 
can then be used to check up correlations obtained in the other 
groups. In this way, too, we get a far more accurate idea of 
the true amount of the correlations among abilities, for people 
in general. It also shows that cases that have been previously 
interpreted as giving negative correlations, would in all proba- 
bility have given small positive correlations if the group chosen 
were representative not of a selected group, but of people of 
all degrees of mental ability chosen at random. In fact, there 
appear to be few if any negative correlations. 

Much labor has been spent upon the correction of Pearson 
coefficients of correlation by means of the Spearman formula. 
The gain in accuracy thus secured does not seem proportionate 
to the amount of time spent. It would be productive of greater 
results to spend more time in getting as accurate and reliable 
records as possible of each individual's ability in each test, so 
that correction on an extensive scale would not be necessary, 
since in any case correction is valid only when the reliability of 
the records themselves is fairly high. 

B — As to facts: 

The most important results are probably the quantitative ones 
presented in Tables IX, X, and XIV, summarizing the correla- 
tion of each test with each of the other thirteen tests used. 

We find justification for the common assumption that there 
is close inter-relation among certain mental abilities, and conse- 
quently a something that may be called ' general mental ability ' 
or ' general intelligence ' ; and that on the other hand certain 
capacities are relatively specialized, and do not necessarily imply 
other abilities except to a very limited extent. 

Of the six varieties of capacity tested, in so far as the tests 
used are representative of them, we find that those most inti- 
mately related to other abilities are (a) selective thinking, (b) 



no Correlations of Mental Abilities 

memory and association, (c) quickness and accuracy of percep- 
tion, (d) motor control, (e) sensory discrimination, each in 
the order named. 

This in turn throws Hght upon the question as to what con- 
stitutes 'general intelligence.' This is a broad term, and may 
be subject to some variation in interpretation. Our Good group 
may not be exactly representative of general intelligence as ex- 
hibited in occupations and callings of a different order from that 
required in leadership in the teaching profession or in an educa- 
tional career. We must also acknowledge limitations in the num- 
ber and variety of tests used. However, subject to these limita- 
tions, we find that ' general intelligence ' implies the different 
abilities tested in the relative order stated in the above para- 
graph — abstract thinking in very high degree, memory and as- 
sociation in less degree, etc. 

We find no justification for the view that ' general intelli- 
gence ' is to be explained on the basis of a hierarchy of mental 
functions, the amount of correlation in each case being due to 
the degree of connection with a common central factor. 

Finally we find that ' general intelligence,' as commonly under- 
stood, can be measured with a high degree of accuracy by the 
use of certain of the tests. In fact, an hour so spent in 
testing an individual gives us a very significant indication of 
his ' general intelligence ' as the term is commonly understood 
and used by well educated people. The time seems not far dis- 
tant when we shall be able to say to a student : " Such and such 
is the order of general mental capacity that we may expect of 
you at the present time. If you do not attain to such and such 
a standard of efficiency, it will be due to other causes than lack 
of mental capacity." 

It would not be difficult to improve at least five of the tests 
used, vis.. Hard Opposites, Ebbinghaus test, Easy Opposites, 
Learning Pairs and Recognizing Forms, to administer them in 
such a way as to make them satisfactory in reliability, and to 
secure norms of performance in each of them. These norms 
could then serve as a basis for comparison, enabling us to se- 
cure important information as to significant phases of the gen- 
eral mental capacity of any individual, which would be of great 
practical value to a prospective employer, or to those directing 
the educational career of the person in question. 



List of Articles Definitely Referred to in this 
Monograph 

AiKENS and Thorndike ('03). Correlations in the Perceptive and Asso- 
ciative Processes. Psychological Review, Vol. IX, p. 374. 

Bagley ('01). On the Correlation of Mental and Motor Ability in School 
Children. American Journal of Psychology, Vol. XII, p. 193. 

BiNET ('99). Attention et Adaptation. L'Annee Psychologique, VI, p. 
248. 

BoNSER ('10). The Reasoning Ability of Children of the Fourth, Fifth 
and Sixth School Grades. New York, Teachers College, Columbia 
University, Contributions to Education, No. 37. 
^''' Brown ('ii). The Essentials of Mental Measurement. London, Cam- 
bridge University Press. 

Burt ('09). Experimental Tests of General Intelligence. British Journal 
of Psychology, Vol. Ill, p. 94. 

NoRSwoRTHY ('o6). The Psychology of Mentally Deficient Children. New 
York, Columbia University. 

Spearman ('04). General Intelligence Objectively Determined and Meas- 
ured. American Journal of Psychology, XV? p. 201. 

Spearman and Krueger ('06). Die Korrelation zwischen verschiedenen 
geistigen Leistungsfahigkeiten. Zeitschrift fur Psychologie, Bd. 
XLIV, s. 50. 

Terman ('06). Genius and Stupidity. Pedagogical Seminary, Xlll, p. 307. 

Thorndike ('09). The Relation of Accuracy in Sensory Discrimination 
to General Intelligence. American Journal of Psychology, Vol. XX, 
p. 364. 

Whipple ('10). Manual of Physical and Mental Tests. Baltimore, War- 
wick and York. 

Whitley ('ii). An Empirical Study of Certain Tests for Individual 
Differences. New York, Columbia University, Archives of Psy- 
chology, No. 19. 

WissLER ('01). The Correlation of Mental and Physical Tests. Psy- 
chological Review, Monograph Supplement, III. 

Bibliography 
For a list of references on Correlation the reader is referred 
to the following publications of recent date: 

G. M. Whipple. Manual of Mental and Physical Tests. Baltimore, War- 
wick and York, 1910. 

William Brown. The Essentials of Mental Measurement. London, 
Cambridge University Press, 1911. 

William Stern. Die Differentielle Psychologie in ihren methodischen 
Grundlagen. Leipsig, 1911. 

Ill 



APPENDIX 

The tests used, the names used in this monograph to designate 
them, and the directions given, in brief, in administering them 
were as follows : 

Test J. "A Test." 

I, a. As quickly as you can, mark all the A's. 
- I, b. " " " " B's. 

GWBTBVKIKSCSAUEBCIWVABZSMDUBKLWHKHYCGYGK 
NANNCBVBSAKOIUPEKCXVGSTVRIWYBYGKHAZLPBYO 
and i5>^ lines more of the same sort. 

Test II. "Geometrical Forms" Test. (See Fig. i, A.) 

II, a. As quickly as you can, mark all the hexagons with the point up, 
thus : M 

II, b. As quickly as you can, mark all the semicircles with the flat side 
up, thus: O 

Test III. "Scroll Test." (See Fig. i, B.) 

III, a. With the fountain pen given, ,trace the space between the black 
lines as quickly as possible without touching the biack. 

Ill, b. Ditto, going faster or slower than in a, as directed. 



112 



Appendix 



"3 



Fig. I 

□QDooDDAOOAaAoagpno^zzDQCbDp 
AZ70DK\ADO'^p<]o<!npnvo\:\noaD;£:n 
^AnvnoDooDc> oqt\nz7c.o> VAODDD 

OQD[I]OAOD^OZ7I>DaoaOZ7c>vnQ0D0 

oiz]Dvc'az7anAonpon[>oS^DODaziDZ7c 

CvxaooDaQDOovDaaAnOoDDDoaDo 

Do^oDAODOo oDZ7'='nooD vs:^'^nz7n 

Donono[>AQDoa^Dn\^oo'=iDDoa)oo 

□o vciO oDOD^ Azynoonn o\^cx)Dod < 

\::\noDZ7nnaoDn'='00'vx^Anggovz7o 

^ODOi>onno^Dnvz7onp<obDDD\::vO 

nn\::^ODDDn"^Df>a^oQc3C3nz7D<i\:\Oc7 

AonnonDD!>o'CiDZ7DZ7ooaoonvag 

o\xoQA[>nnao'^DZ7VQnon^ooz7D 

nnoD\Anooooo'='Z7Donaox^oDono^ 

VADO^QnOOnoODDOO^QODQ'^a^^A 



A. 

AG VOO 
OASOG 




C. 



□ O^QPOOVOi] 
D. 



ziNy0o 
liumuar^ 



^EBliliC0UnZi» 
03n^NS:3ZEfIT] 

F 



114 



Correlations of Mental Abilities 



Test IV. "Easy Opposites" Test. 

IV, a. As quickly as possible give orally a word that means the exact 
opposite of each word in the list. 

IV, b. Ditto with second list. 

IV, c. " " third " . 

IV. d. " " fourth " . 



IV, a 


IV, t 


IV. c 


IV, d 


good 


stale 


high 


day 


outside 


hot 


up 


asleep 


quick 


dirty 


wet 


absent 


tall 


heavy 


new 


brothel 


big 


late 


soft 


best 


loud 


first 


wider 


over 


white 


left 


wrong 


big 


light 


morning 


yes 


backwards 


happy 


much 


young 


buv 


false 


. near 


brave 


come 


like 


north 


winter 


cheap 


rich 


open 


weak 


broad 


sick 


in 


forget 


dead 


glad 


sharp 


wila 


land 


thin 


east 


beginning 


country 


empty 


sour 


straight 


tall 


war 


something 


raise 


son 


many 


stay 


rough 


here 


above 


push 


love 


less 


friend 


nowhere 


noisy 


easy 



Test V. "Recognising Forms" Test. (See Fig. i, C, D, E and F.) 

V, a, I (C of Fig. i). You may study this for i minute; then I shall 
tell you to stop. (The general nature of the test and what was to be done 
by the subject were explained before starting.) 

V, a, 2 (D of Fig. i). Mark all the forms exactly the same as those 
seen in V, a, i. (No time limit was required in the marking.) 

V, b, I (E of Fig. i). You may study this for one and a half minutes; 
then I shall tell you to stop. 

V, b, 2 (F of Fig. i). Mark all the forms exactly the same as those 
seen in V, b, i. (No time Hmit was required in the marking.) 



Appendix 



115 



Test VI. "Memory of Words" Test. 

VI, a. Write down all the words in the list that you can remember 
after hearing them read once. 

VI, b. Ditto with second list, VI, b, etc. 



VI, a 


VI. b 


VI, c 


VI. d 


picture 


knife 


mouse 


whisper 


silly 


window 


' bank 


Columbus 


unless 


peacock 


disease 


necessary 


lizard 


brass 


cheap 


laugh 


book 


weary 


country 


dictionary 


pain 


rich 


study 


cane 


island 


vine 


tooth 


key 


tin 


servant 


musician 


doctor 


literature 


pinch 


pie 


boat 


axe 


wheel 


building 


enough 


run 


hammock 


fruit 


walking 


tomato 


horn 


weapon 


rent 


tired 


pitiless 


spider 


earth 


frost 


crack 


mountain 


canvas 


wide 


beef 


shallow 


carpet 


Indian 


glue 


window 


steam 



Test VII. "Learning Pairs." (See Fig. 2.) 

Study VII, a, i, for one minute sa that when VII, a, 2, is given, you 
can write down the corresponding word. Similarly with VII, b, i and b, 2. 
Similarly with VII, c and d (except that one and a half minutes were 
allowed for study instead of one minute). For Fig. 2, the lists of pairs 
are given in order. 

Test VIII. "Memory of Passages." 

Write down all that you can remember of the substance of the passage 
after hearing it read once. 



VIII, a. Memory of Passages 
It isn't necessary to read a book in order to be happy with it. On a 
steamer or in a hammock you simply have to have the book in your lap 
or close at hand, with the paper-cutter and pencil. It must be the sort of 
book you like. You open it and read the table of contents. A deep peace 
fills your soul. Here is this delicious book and the whole day, both yours. 
You lean back to think of books by these men and by others that you 
already know and love. Memory brings you one beautiful picture after 
another. 

VIII, b. Memory of Passages 
Thirty-two passengers were injured, none of them seriously, by the 
derailment of the Chattanooga and Washington Limited train on the 



1 16 Correlations of Mental Abilities 

Fig. 2 



«d> '^^ 


y^ 


^(T grit 


^^ 


-{""Y^ vast 


^ 


y-|j atnt 


^ 


P7 wll 


-^ 


^Pp Wag 


^^^ 


£^ <ju!tite 


J> 


^ t^laca 


^ 


^i^ tooa 


^ 


>Q«^9 


)^^ 


fV- ^J'-i- 


/-^ 


QA, n^m^L 


>tr 


/-M t-«l 


rrs 


^^ ckirm 


^ 


rrs ^^te 


\^ 


^ Jokn 


QCs 


^3j1- James 


-rV 


;^ yet 


y->j 


^ {irats 


■^ 


>tr I'- 


>m 


VII. a, 1. 


VII. a, 2. 


VII. b, 1. 


VII. b, 2 


l^ k«lti. 


W 


C^ UmU 


^ 


^N^ 9^t. 


^>II] 


c{_^ f.ss 


^ 


^ V.1 


t^ 


JV -" 


^ 


l>l!^ two 


l^ 


^ real 


^ 


/^ rank 


^> 


^VT" t""-!! 


c:^ 


-^coal 


^ 


\£ Frod 


w 


X_i(^ nice 


O- 


^ aft 


,5V 


T^ marcK 


7-^ 


^< kerl, 


-e^< 


•^ crsae 


T^ 


kA^ learn 


(^ 


C/^ f ™- 


^ 


>^ dead 


u^ 


VII. c, 1. 


VII. c, 2. 


VII. d, 1. 


VII. d, 2. 



Southern Railway, thirty miles south of Charlottesville, and just north 
of Ryan's Siding, Virginia, early to-day. A broken rail was the cause of 
the accident. 

The entire train composed of a baggage car, day coach and three sleep- 
ers, left the track, the sleepers being almost destroyed by fire. A special 
train was quickly made up and proceeded to this city with all the passen- 
gers of the Limited. The wreck blocked the track for several hours, all 
trains meanwhile being detained. 

VIII, c, Memory of Passages 
Langford of the Three Bars, as the title suggests, is a story of the West 
depicting cowboy life. The scenes are in South Dakota of the time of the 
" rustlers," who cared for neither the interference of man nor law. The 
action turns round the Three Bars Ranch, which is run by Paul Langford, 
" a man — a godlike type with his sunny hair and his great strength," whose 



Appendix 117 

object it is to do away with the cattle thieves headed by Jesse Black. He 
is aided by Gordeti, the county attorney, and Jim Munson, a real cowboy. 

VIII, d. Memory of Passages 
One morning a couple of Springs ago, if any of your readers had chanced 
this way, they might have seen me coming from the vineyard with two 
bluebirds, one in each hand. The birds were well and vigorous and en- 
tirely unharmed. If questioned I might have explained that I went down 
into the vineyard and picked the birds up off the 'ground, where they had 
the full possession of their wings, and that there are times when it is not 
difficult for me to do such things. These birds were of the species known 
as the Least-flycatcher, or Chebeck Bird. 

Test IX. "Drawing Lengths." 

I. To the right of i, draw in succession three lines each equal in length 
to I. You may add to, or take away from, the line you have drawn, as 
much as necessary in order to get it the required length. 

Similarly with lines 2 and 3. (Lines i, 2 and 3 were 100, 75 and 50 
millimeters long respectively.) 

Test X. "Estimating Lengths." 

Which line is the longer? (Two lines drawn end to end horizontally 
on a long piece of white card-board were shown.) In case of the first 
8 lines thus shown on the card-board, one line was 108 mm. in length, 
and the other 100 mm. In case of the second set of 8 pairs of lines, one 
line was 106 mm. and the other 100. In the third set, one was 104 and the 
other 100; and in the fourth set one was 102 and the other 100 mm. The 
whole test was then repeated. 

Test XL "Adding." 

Add the ten sums in XI, a, as quickly and accurately as you can, writing 
down the results as you get them. 

Similarly with XI, b. 

XIa. Addition 

17 26 27 72 23 

42 51 24 13 47 

38 47 83 39 86 

91 82 19 81 54 

54 63 45 26 36 



17 


42 


38 


91 


36 


26 


51 


47 


82 


26 


27 


24 


83 


19 


45 


72 


14 


39 


62 


63 


23 


47 


86 


54 


54 



ii8 



Correlations of Mental Abilities 



41 
52 
86 
23 
35 



63 
67 
34 

78 
19 



Xlb. Addition 

67 
86 
23 
45 
67 



78 
37 
96 
72 
23 



86 
32 
44 
36 
68 



45 


52 


19 


45 


23 


13 


86 


78 


67 


92 


68 


23 


67 


78 


36 


77 


35 


23 


37 


68 


86 


67 


86 


96 


39 



Test XII. "Hard Opposites." 

Write as quickly as you can beside each word in the column a word 
that means the exact opposite of it. Do the best you can with each word 
rather than leave the space blank. 





Hard Opposites 




XII, b 


XII, a 


XII, d 


XII, c 


serious 


vertical 


succeed 


tender 


grand 


ignorant 


strict 


animated 


clumsy 


rude 


tardy 


proficient 


to win 


simple 


sleepy 


impoverish 


to respect 


deceitful 


suspicious 


cruel 


frequently 


stingy 


rigid 


generous 


to lack 


permanent 


suave 


haughty 


apart 


over 


sinful 


silly 


stormy 


to degrade 


conservative 


insignificant 


motion 


weary 


refined 


disastrous 


forcible 


to spend 


pride 


miser 


to float 


to reveal 


despondent 


result 


straight 


genuine 


imaginary 


hindrance 


to hold 


level 


beautiful 


strength 


after 


broken 


injurious 


innocent 


unless 


wild 


diligent 


busy 


rough 


part 


sell 


remember 


to bless 


past 


sure 


increase 


to take 


permit 


active 


preserve 


exciting 


precise 


venturesome 


belief 



Test XIII. " Completing Words," or " Ba-test." 

As quickly as possible, add any letter or letters to each syllable in the 
list, so as to make it a complete word. 



Appendix 119 

Completing Words 



a. 






b. 


c. 




c 


1. 


ba 


be 


bi 


bo 


ab 


ea 


ic 


ao 


ca 


ce 


ci 


CO 


ac 


eb 


id 


ob 


da 


de 


di 


do 


ad 


ec 


ig 


oc 


fa 


fe 


fi 


fo 


af 


ed 


il 


od 


ga 


ge 


gi 


go 


ag 


ef 


im 


of 


ha 


he 


hi 


ho 


al 


ei 


in 


ol 


ja 


je 


ji 


jo 


am 


el 


ir 


om 


la 


ke 


ki 


lo 


an 


em 


is 


on 


ma 


le 


li 


mo 


ap 


en 


it 


op 


na 


me 


mi 


no 


ar 


ep 


iv 


or 


pa 


ne 


ni 


po 


as 


eq 


um 


OS 


ra 


pe 


pi 


ro 


at 


er 


un 


ot 


sa 


re 


ri 


so 


au 


es 


up 


ou 


ta 


se 


si 


to 


va 


ev 


ur- 


ov 


va 


te 


ti 


vo 


aw 


ex 


us 


ow 



Test XIV. " Ebbinghaus Mutilated Text." 

(The subject was first shown what was to be done on a sample sheet 
similar to the ones given below.) 

Fill in each blank with the word that will make the best sense. Do the 
work as well and as quickly as you can. Put only one word in each blank 
space. 

Test XIV, a. Ebbinghaus Mutilated Text. 

Park Hill on the Hudson offers you a solution of the home problem 
to-day. No home seeker or investor can afford to ignore its claims. 
Escape the wear and tear of the city's noise and rush in this open air para- 
dise, just at the city's edge, in all respects an ideal home location for your- 
self and family. 

There are cottages containing every improvement waiting for you to 
step in and make yourself comfortable. It not only commands the most 
beautiful view around New York but is protected for all time against 
intrusion. Choice lots now selling on very easy terms. 

Test XIV, b. Ebbinghaus Mutilated Text. 

We believe we can prove to you that this investment is so secure and 
the dividends so sure, that it justifies you in withdrawing money from 
the Savings Banks, where it is earning 3^% and putting it in our busi- 
ness where it will earn 7%. We are a New England enterprise, managed 
by New England men, and we have behind us a record of fourteen years 
of unbroken success. Whether you have much or little you cannot afford 
to let slip this opportunity of doubling the income from your savings. 
Prompt action in this matter will repay you well. 

Test XIV, c. Ebbinghaus Mutilated Text. 

On the contrary, it didn't cost me a dollar. In fact, though at times 
I have found myself possessed of considerable sums of ready money, I 



I20 



Correlations of Mental Abilities 



have never been a man of property in the strict sense of the word. I 
abandoned my profession, the law, as I did not find its practice so lucra- 
tive as I had hoped. For some years thereafter I travelled largely on the 
Mississippi River. It was the decline in steamboating and the adoption of 
less leisurely methods of travel that cut into my income and forced me 
to come North and engage in trade. 

Test XIV, d. Ebbinghaus Mutilated Text. 

The occult in everyday affairs is the theme of this new book by Robert 
Chalmers. Opening one of the thrilling stories of whicli the volume is 
composed is the tale of some awful mysterious happening, some super- 
natural event beyond the power of material reasoning of mortal man to 
explain, which comes into the life of some ordinary, everyday man. The 
opening chapter tells of a dinner given to a man deeply versed in occult- 
ism by his American friends. To these he gives many hints and sugges- 
tions of momentous things which he can plainly see waiting for them in 
the future. 

Test XIV, e. Ebbinghaus Mutilated Text. 

I asked the slovenly, hut cheerful female who answered the bell for 
the landlady; wondering the while zvhat I should say when I was asked 
for references. The merriment had not been called forth by anything 
amusing in my appearance, as my vanity had feared, bnt by a story which 
a man sitting at the head of the table was just finishing. The only vacant 
chair in the room was beside him, and, rather awkwardly, for I felt that 
they were taking my measure, I made my way toward it. As I sat down 
he greeted me with a polite bow. 

Test XIV, f. Ebbinghaus Mutilated Text. 

If we are perfectly well, thoroughly sound, we need not be depressed. 
The perfectly healthy animal has no worries. The remedy has already 
been indicated. Regretfully it is so simple that very few people take the 
trouble to apply it. When it is clearly and widely recognized that vuorry 
is stupid, that its cure is simple where there is no organic trouble, worry 
will cease. Worry is simply a form of what for the sake of a nice large 
word, is called " neurasthenia," nerve-depletion. 

Given plenty of recreation, plenty of fresh air, and the nor>nal man will 
not worry. 

Test XIV, g. Ebbinghaus Mutilated Text. 

We confess to something of sympathy zvith the correspondent zvho 
hinted yesterday that ivhcn children are run over and killed by automo- 
biles, the fault is not always that of the automobilist, but sometimes rests 
in some measure on those who do not teach their children to avoid un- 
necessary danger. It is a plain fact, of course, that public highways are 
for the use of the whole population, and that the automobilist is under 
every obligation to keep the limitations of his rights and privileges in 
mind as he ^oes along, but the road is his as well as other people's. 



Appendix 121 

Test XIV, h. EbbingJiaus Mutilated Text. 

A law in defence of property rights in the broadest sense if observed 
would almost abolish international conflicts. Gentlemen do not fight with 
fists in money dififerences nor do they refer them to courts of honor. Civil 
courts are for that purpose and are as useful for nations as for men. 
The sanction of international law must be merely moral, for a long time 
at least. But in order that there should be any moral sanction there must 
be a moral code. The principles of such a code are deducible fi'om 
treaties to which nations have set their hands and seals. 

Test XV. "Absurdities." 

As quickly as possible mark each sentence that contains an absurdity 
or impossibility. For instance, if a sentence stated or implied that ordi- 
nary lead was floating on water, mark such a sentence as impossible or 
absurd. Do not mark the sentences that contain no absurdity or imposssi- 
bility. 

Test XV, a. Absurdities. 

1. Though armed only with his little dagger, he brought down his 
assailant with a single shot. 

2. Silently the young dude hurried on, in spite of the darkness, and 
went splash into a puddle on the roadside. 

3. Having reached the goal I looked back and saw my opponents still 
running in the distance. 

4. While walking backwards he struck his forehead against a wall, and 
was knocked insensible. 

5. Offended by his obstinate silence, she refused to listen to him further. 

6. With his sword he pierced his adversary who fell dead. 

7. The one-armed cripple was attacked by a dog, which seized his 
wrist, but he pushed it ofif with the other hand. 

8. While forcing my way through the crowd, I came suddenly upon an 
old friend. 

Test XV, b. Absurdities. 

1. The dogs pursued the stag through flower gardens in full bloom. 

2. The storm which began yesterday morning, has continued without 
intermission for three days. 

3. That day we came in sight of several icebergs that had been entirely 
melted by the warmth of the Gulf Stream. 

4. While sharpening his three-bladed knife, my cousin cut his middle 
finger. 

5. My friend pointed out the North Star clearly visible on our right as 
we walked briskly eastward in the moonlight. 

6. The red haired girl, standing in the corner, is taller than any of her 
brothers. 

7. The two towns were separated only by a narrow stream, which was 
frozen over all winter. 

8. Fearing that he might waken her patient by his impudent talk, the 
nurse gave the detested dummy what he wished. 



122 



Correlations of Mental Abilities 



Test XV, c. Absurdities. 

1. After dressing herself carefully and elaborately, she descended to 
the breakfast-room, only to find it deserted. 

2. Preferring a tarnished reputation to the probability of becoming a 
corpse for the rest of his life, the young soldier took to flight. 

3. Upon very careful testing it has been found that a pint of cream 
weighs slightly more than a pint of milk. 

4. The old soldier energetically shouldered his crutch like a gun, as 
he talked by the fireside. 

5. In the busiest sections of New York City, cheap houses, like rare 
jewels, are scarce and expensive. 

6. In the ruins of an ancient Roman city there has recently been dis- 
covered a small skull believed to have been that of Pontius Pilate when 
he was about ten years old. 

7. We serve hot and cold lunches on five minutes' notice, to first and 
second class passengers. 

8. In my excitement I caught a glimpse of the sharp features of my. 
enemy, who had just passed around the corner. 



Test XV, d. Absurdities. 

1. Our horse grew so tired that finally we were compelled to walk up 
all the hills. 

2. The hands of the clock were set back, so that the meeting might 
surely close before sunset. 

3. In some states there is a law forbidding a man to marry his widow's 
sister. 

4. Don't go to unreliable real estate offices to be swindled, come in here. 

5. Owing to the lack of ready money, the shrewd financier was unable 
to take advantage of the rare bargains then offered. 

6. Travellers who cannot read should be directed to sources of reliable 
information by signs printed in conspicuous places along the roads of 
travel. 

7. With wrapt attention, though the audience was immense, the orator 
listened to the crowd addressing him. 

8. Our office boy has beqn coming early of late, for he was often be- 
hind before, because his watch was slow. 



VITA 

Benjamin Roy Simpson was born August 13, 1877, at 
Drumbo, Ontario, Can. 

Academic education : Woodstock College, Woodstock, Ont., 
'92-95 ; B. A. degree, mathematical course of McMaster Univer- 
sity, Toronto, Ont., '99. 

Graduate work: Ontario Normal College, Hamilton, Ont., 
'99-'oo; Graduate Scholar, University of Chicago, 'o5-'o6; 
Teachers College, New York City, 'o6-'o8; Research Scholar, 
'o7-'o8. 

Professional experience: Elementary Schools of Victoria, 
B. C, and Principal of Wellington Public Schools, 'oo-'o2 ; Prin- 
cipal Cumberland High School, Cumberland, B. C, 'o2-'o5 ; 
Teacher of Psychology and Principles of Education, Brooklyn 
Training School for Teachers, 'o8-'i2; Lecturer in Psychology 
and in Educational Theory, University of Georgia Summer 
School, '09. 

Sometime contributor to the New Students' Reference Work. 



CORRELATIONS OF MENTAL 
ABILITIES 



BY 
BENJAMIN R. SIMPSON, 



Submitted in partial fulfilment of the requirements 
for the degree of Doctor of Philosophy, in the 
Faculty of Philosophy, Columbia University. 



PUBLISHED BY 

OIparI|prs Olnlkge, ffinlttmbia 3lntti^rattu 

NEW YORK CITY 

1912 



LEJa'!3 



i- . 



